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ML Aggarwal Solution Class 10 Chapter 5 Quadratic Equations in One Variable MCQs

MCQs

Question 1

Which of the following is not a quadratic equation ?

(a) (x+2)²=2(x+3)

(b) x²+3x=(–1) (1–3x)

(c) (x+2)(x–1)=x²–2x–3

(d) x³–x²+2x+1=(x+1)3

Sol :

(a) (x + 2)² = 2(x + 3)

⇒ x² + 4x + 4 = 2x + 6

⇒ x² + 4x – 2x + 4 – 6 = 0

⇒ x² + 2x – 2

It is a quadratic equation.

(b) $x^{2}+3 x=(-1)(1-3 x) $

$\Rightarrow x^{2}+3 x=-1+3 x$

$\Rightarrow x^{2}+1=0$

It is also quadratic equation.

$x^{2}-x+2 x-2=x^{2}-2 x-3$

$x^{2}-x^{2}+x+2 x-2+3=0 \Rightarrow 3 x+1=0$

It is not a quadratic equation.

(d) $x^{3}-x^{2}+2 x+1=(x+1)^{3}$

$=x^{3}+3 x^{2}+3 x+1$

$x^{3}-x^{2}+2 x+1$

$3 x^{2}+x^{2}-2 x-1+3 x+1=0$

$\Rightarrow 4 x^{2}+x=0$

It is a quadratic equation

Ans : (c)

Question 2

Which of the following is a quadratic equation ?

(a) (x – 2) (x + 1) = (x – 1) (x – 3)

(b) $(x+2)^{3}=2 x\left(x^{2}-1\right)$

(c) $x^{2}+3 x+1=(x-2)^{2}$

(d) $8(x-2)^{3}=(2 x-1)^{3}+3$

Sol :

(a) (x – 2) (x + 1) = (x – 1) (x – 3)
⇒ x2 + x – 2x – 2 = x2 – 3x – x + 3
⇒ 3x + x – 2x + x = 3 + 2
⇒ 3x = 5
It is not a quadratic equation.

(b) $(x+2)^{3}=2 x\left(x^{2}-1\right)$

$x^{3}+6 x^{2}+12 x+8=2 x^{3}-2 x$

$x^{3}+6 x^{2}+12 x+8-2 x^{3}+2 x=0$

$-x^{3}+6 x^{2}+14 x+8=0$

It is not a quadratic equation.

$x^{2}+3 x+1=x^{2}-4 x+4$

⇒3x+1+4 x-4=0

⇒7x-3=0

It is not a quadratic equation.

(d) $8(x-2)^{3}=(2 x-1)^{3}+3$

$8\left(x^{3}-6 x^{2}+12 x-8\right)$

$=8 x^{3}-12 x^{2}+6 x-1+3$

$8 x^{3}-48 x^{2}+96 x-64-8 x^{3}+12 x^{2}-6 x+1-3=0$

$-36 x^{2}+90 x-66=0$

It is a quadratic equation

Ans : (d)

Question 3

Which of the following equations has 2 as a root ?

(a) $x^{2}-4 x+5=0$

(b) $x^{2}+3 x-12=0$

(c) $2 x^{2}-7 x+6=0$

(d) $3 x^{2}-6 x-2=0$

Sol :

(a) $x^{2}-4 x+5=0$

$\Rightarrow(2)^{2}-4 x^{2}+5=0$

⇒ 4 – 8 + 5 = 0

⇒ 9 – 8 ≠ 0

2 is not its root.

(b) $x^{2}+3 x-12=0$

$ \Rightarrow(2)^{2}-3 \times 2-12=0$

⇒4-6-12=4-18=-14

∴ 2 is not its roots.

$ \Rightarrow 2(2)^{2}-7 \times 2+6=0$

⇒ 8-14+6=0 $

⇒0=0

∴ 2 is its root

(d) $3 x^{2}-6 x-2=0$

$ \Rightarrow 3(2)^{2}-6 \times 2-2=0$

⇒12-12-2=0

⇒12-14=0

∴ 2 is not its root.

Ans : (c)

Question 4

If $\frac{1}{2}$ is a root of the equation $x^{2}+k x-\frac{5}{4}=0$ then the value of k is

(a) 2

(b) – 2

(c) $\frac{1}{4}$

(d) $\frac{1}{2}$

Sol :

$\frac{1}{2}$ is a root of the equation

$x^{2}+k x-\frac{5}{4}=0$

Substituting the value of $x=\frac{1}{2}$ in the equation

$\left(\frac{1}{2}\right)^{2}+k \times \frac{1}{2}-\frac{5}{4}=0$

$\Rightarrow \frac{1}{4}+\frac{k}{2}-\frac{5}{4}=0$

$\Rightarrow \frac{k}{2}-1=0$

⇒k=1×2=2

∴k=2

Ans (a)

Question 5

If $\frac{1}{2}$ is a root of the quadratic equation $4 x^{2}-4 k x+k+5=0$ then the value of k is

(a) – 6

(b) – 3

(c) 3

(d) 6

Sol :

$\frac{1}{2}$ is a root of the equation

$4 x^{2}-4 k x+k+5=0$

Substituting the value of $x=\frac{1}{2}$ in the equation

$4\left(\frac{1}{2}\right)^{2}-4 \times k \times \frac{1}{2}+k+5=0$

1-2k+k+5=0

-k+6=0

k=6

Ans (d)

Question 6

The roots of the equation $x^{2}-3 x-10=0$ are

(a) 2,- 5

(b) – 2, 5

(c) 2, 5

(d) – 2, – 5

Sol :

$x=\frac{-(-3) \pm \sqrt{(-3)^{2}-4 \times 1 \times(-10)}}{2 \times 1}$

$=\frac{3 \pm \sqrt{9+40}}{2}=\frac{3 \pm \sqrt{49}}{2}=\frac{3+7}{2}$

∴$x=\frac{3+7}{2}=5$ and $x=\frac{3-7}{2}=\frac{-4}{2}=-2$

x = 5, – 2 or – 2, 5

Ans (b)

Question 7

If one root of a quadratic equation with rational coefficients is $\frac{3-\sqrt{5}}{2}$, then the other

(a) $\frac{-3-\sqrt{5}}{2}$

(b) $\frac{-3+\sqrt{5}}{2}$

(c) $\frac{3+\sqrt{5}}{2}$

(d) $\frac{\sqrt{3}+5}{2}$

Sol :

One root of a quadratic equation is $\frac{3-\sqrt{5}}{2}$ then other root will be $\frac{3+\sqrt{5}}{2}$

Ans (c)

Question 8

If the equation $2 x^{2}-5 x+(k+3)=0$ has equal roots then the value of k is

(a) $\frac{g}{8}$

(b) $-\frac{g}{8}$

(c) $\frac{1}{8}$

(d) $-\frac{1}{8}$

Sol :

$2 x^{2}-5 x+(k+3)=0$

a=2, b=-5, c=k+3

=25-8(k+3)

∴ Roots are equal.

$\therefore b^{2}-4 a c=0$

∴ 25-8(k+3)=0

⇒25-8k-24=0

⇒1-8k=0

⇒8 k=1

$\therefore k=\frac{1}{8}$

Ans (c)

Question 9

The value(s) of k for which the quadratic equation $2 x^{2}-k x+k=0$ has equal roots is (are)

(a) 0 only

(b) 4

(c) 8 only

(d) 0, 8

Sol :

$2 x^{2}-k x+k=0$

a=2, b=-k, c=k

$\therefore b^{2}-4 a c=(-k)^{2}-4 \times 2 \times k$

$\quad=k^{2}-8 k$

∴ Roots are equal. $\therefore b^{2}-4 a c=0$

$k^{2}-8 k=0$

⇒k(k-8)=0$

Either k=0

or k-8=0, then k=8

k=0,8

Ans (d)

Question 10

If the equation $3 x^{2}-k x+2 k=0$ roots, then the the value(s) of k is (are)

(a) 6

(b) 0 Only

(c) 24 only

(d) 0

Sol :

$3 x^{2}-k x+2 k=0$

Here, a=3, b=-k, c=2 k

$b^{2}-4 a c=(-k)^{2}-4 \times 3 \times 2 k$

$=k^{2}-24 k$

∴ Roots are equal. $\therefore b^{2}-4 a c=0$

$\therefore k^{2}-24 k=0$

⇒k(k-24)=0

Either k=0

or k-24=0, then k=24

∴ k=0, 24

Ans (d)

Question 11

If the equation $\{k+1\} x^{2}-2(k-1) x+1=0$ has equal roots, then the values of k are

(a) 1, 3

(b) 0, 3

(c) 0, 1

(d) 0, 1

Sol :

(k + 1)x² – 2(k – 1)x + 1 = 0

Here, a = k + 1, b = -2(k – 1), c = 1

$\therefore b^{2}-4 a c=[-2(k-1)]^{2}-4(k+1)(1)$

$\quad=4\left(k^{2}-2 k+1\right)-4 k-4$

$\quad=4 k^{2}-8 k+4-4 k-4$

$\quad=4 k^{2}-12 k$

∵ Roots are equal. $\therefore b^{2}-4 a c=0$

$\therefore 4 k^{2}-12 k=0$

⇒4 k(k-3)=0

⇒ k(k-3)=0

Either k=0 or k-3=0, then k=3

k=0,3(b)

Question 12

If the equation 2x² – 6x + p = 0 has real and different roots, then the values ofp are given by

(a) $p<\frac{9}{2}$

(b)p $\leq \frac{9}{2}$

(d) $p \geq \frac{9}{2}$

Sol :

2x² – 6x + p = 0

Here, a = 2, b = -6, c = p

$b^{2}-4 a c=(-6)^{2}-4 \times 2 \times p$

=36-8 p

∵ Roots are real and unequal.

$\therefore b^{2}-4 a c>0$

⇒ 36-8p>0

⇒ 36>8p

⇒ $\frac{36}{8}>p$

⇒ $p<\frac{36}{8}$

⇒ $p<\frac{9}{2}$

Ans (a)

Question 13

The quadratic equation 2x² – √5x + 1 = 0 has

(a) two distinct real roots

(b) two equal real roots

(c) no real roots

(d) more than two real roots

Sol :

2x² – √5x + 1 = 0

Here, a = 2, b = -√5, c = 1

$b^{2}-4 a c=(-\sqrt{5})^{2}-4 \times 2 \times 1$

=5-8=-3

$\because b^{2}-4 a c<0$

∵ It has no real roots.

Question 14

Which of the following equations has two distinct real roots ?

(a) $2 x^{2}-3 \sqrt{2 x}+\frac{9}{4}=0$

(b) $x^{2}+x-5=0$

(c) $x^{2}+3 x+2 \sqrt{2}=0$

(d) $5 x^{2}-3 x+1=0$

Sol :

(a) $2 x^{2}-3 \sqrt{2} x+\frac{9}{4}=0$

$b^{2}-4 a c=(-3 \sqrt{2})^{2}-4 \times 2 \times \frac{9}{4}=18-18=0$

∵ Roots are real and equal.

(b) $x^{2}+x-5=0$

$b^{2}-4 a c=(1)^{2}-4 \times 1 \times(-5)$

$=1+20=\sqrt{21}>0$

Roots are real and distinct.

Ans (b)

Question 15

Which of the following equations has no real roots ?

(a) x² – 4x + 3√2 = 0

(b) x² + 4x – 3√2 = 0

(c) x² – 4x – 3√2 = 0

(d) 3x² + 4√3x + 4 = 0

Sol :

(a) x² – 4x + 3√2 = 0

b² – 4ac = ( -4)² – 4 × 1 × 3√2

= 16 – 12√2

= 16 – 12(1.4)

= 16 – 16.8

= -0.8

b² – 4ac < 0

Roots are not real.

Ans (a)

ML AGGARWAL CLASS 12 Chapter 2 Inverse Trigonometric Functions Exercise 2.1 (CBSE)

Exercise 2.1

Very short answer type questions (1 to 21) :

Question 1

Sol :

ML AGGARWAL CLASS 12 Chapter 1 Relations and Functions Exercise 1.2 (CBSE)

Exercise 1.2

Question 1

Sol :

ML AGGARWAL CLASS 12 Chapter 1 Relations and Functions Exercise 1.1 (CBSE)

Exercise 1.1

Question 1

Determine whether each of the following relations are reflexive, symmetric and transitive :

(i) Relation R in the set A = {1, 2, 3, …, 10} defined by R = {(x, y) : 2x – y = 0}.

(ii) Relation R in the set Z of all integers defined by

R = {(x, y) : x – y is an integer}

(iii) Relation R in the set N of all natural numbers defined by

R = {(x, y) : y = x + 5, x < 4}.

Sol :

Question 2

If the relation R in the set A, where A = {1, 2, 3, 4, 5, 6}, is defined by R = {(x, y) : y is divisible by x}, then express R in the roster form. Also determine whether the relation R is

(i) reflexive (ii) symmetric (iii) transitive.

Sol :

Question 3

If R is the relation defined on the set of natural numbers N as follows:

R = {(x, y); x, y ∈ N, 2x + y = 41},

find the domain and the range of the relation R.

Determine whether the relation is reflexive, symmetric and transitive.

Sol :

Question 4

Determine whether each of the following relations in the set A of human beings in a city at a particular time are reflexive, symmetric and transitive :

(i) R = {(x, y) : x and y work at the same place}.

(ii) R = {(x, y) : x and y live in the same locality}.

(iii) R = {(x, y) : x is exactly 5 cm taller than y}.

(iv) R = {(x, y) : x and y live within 2 kilometres}.

(v) R = {(x, y) : x is wife of y}.

Sol :

Question 5

Determine whether each of the following relations in the set A of students at a particular time are symmetric and transitive:

(i) R = {(x, y) : x, y ∈ A, x and y are honest}

(ii) R = {(x, y) : x, y ∈ A, x and y are obedient}

(iii) R = {(x, y) : x, y ∈ A, x and y are hardworking}

What are the advantages of students being honest, obedient and hardworking?

Sol :

Question 6

Show that the relation R in the set A = {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} is reflexive but neither symmetric nor transitive.

Sol :

Question 7

Decide in each of the following cases whether the relation is symmetric, transitive and reflexive. Justify your answer by giving examples.

(i) ‘Is less than’ on N

(ii) ‘Is a factor of’ on N

Sol :

Question 8

Let T be the set of all triangles drawn in a plane with R as a relation in T given by $R = {(T_1, T_2) : T_1 ≅ T_2}$. Show that R is an equivalence relation.

Sol :

Question 9

Show that the relation R in the set A of all books in a library of a school, given by

R = {(x, y) : x and y have same number of pages}, is an equivalence relation.

Sol :

Question 10

Show that the relation R in the set A of points in a plane, given by R = {(P, Q) : points P and Q have equal distances from the origin}, is an equivalence relation. Also show that the set of all points related to a point P (different from origin) is the circle passing through P with origin as its centre.

Sol :

Question 11

Show that the relation R in the set A of all triangles, given by $R = {(T_1, T_2) : T_1 ~ T_2}$, is an equivalence relation. Consider three triangles $T_1$ with sides 3, 4, 5; $T_2$ with sides 5, 12, 13 and $T_3$ with sides 6, 8, 10. Which triangles among $T_1$, $T_2$ and $T3_$ are related?

Sol :

Question 12

Show that the relation R in the set A of all polygons, given by $R = {(P_1, P_2) : P_1$ and $P_2$ have same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right triangle T with sides 3, 4 and 5?

Sol :

Question 13

Show that the relation R defined in the set L of all straight lines drawn in the XY-plane, given by $R = {(L_1, L_2) : L_1 \text{ is parallel to }L_2}$, is an equivalence relation. Find the set of all straight lines related to the line y = 2x + 4.

Sol :

Question 14

Show that the relation R on the set I of all integers defined by R = {(a, b) : a – b is divisible by 3, a, b ∈ I} is an equivalence relation

Sol :

Question 15

Let I be the set of all integers and R be the relation on I defined by R = {(a, b) : a – b is divisible by 5}. Prove that R is an equivalence relation. Find the set of all elements of I related to 1.

Sol :

Question 16

Give examples of relations which are

(i) symmetric but neither reflexive nor transitive.

(ii) transitive but neither reflexive nor symmetric.

(iii) symmetric and transitive but not reflexive.

(iv) symmetric and reflexive but not transitive.

(v) reflexive and transitive but not symmetric.

Sol :

Question 17

Give an example of a relation R on A = {a, b, c} which is

(i) neither reflexive nor symmetric but transitive.

(ii) neither symmetric nor transitive but reflexive.

(iii) neither transitive nor reflexive but symmetric.

Sol :

Question 18

Show that the relation R in the set A = {1, 2, 3, 4, 5}, given by R = {(a, b) : |a – b| is even}, is an equivalence relation. Also show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other but no element of {1, 3, 5} is related to any element of {2, 4}.

Sol :

Question 19

Show that the relation S in the set A = {x ∈ Z : 0 ≤ x ≤ 12} given by

S = {(a, b) : a, b ∈ A, | a – b | is divisible by 4} is an equivalence relation.

Find the set of elements related to 1

Sol :

Question 20

Show that the relation R in the set A = {x ∈ W, 0 ≤ x ≤ 17} given by

(i) R = {(a, b) : |a – b| is a multiple of 5}

(ii) R = {(a, b) : a = b}

are equivalence relations. Find the set of all elements related to 2 in each case.

Sol :

Question 21

Consider the division of set A = {1, 2, 3, 4, 5, 6, 7, 8} by subsets {1, 6}, {2, 7}, {3, 8}, {4} and {5}. Show that the relation R in A, given by R = {(a, b) : a and b lie in the same subset of the division of A}, is an equivalence relation. Find the set of all elements of A related to 6 and the set of all elements related to 5.

Sol :

Very Short Answer Type Question

Question 22

If A = {– 1, 1, 3}, then what is the number of relations on A?

Sol :

Question 23

Let A be any non-empty set. State true or false :

(i) Identity relation on A is reflexive.

(ii) Every reflexive relation on A is identity relation on A.

(iii) Identity relation on A is symmetric.

(iv) Identity relation on A is an equivalence relation.

(v) Universal relation on A is an equivalence relation

Sol :

Question 24

State the reason for the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} not to be transitive.

Sol :

Question 25

If A = {0, 1, 2, …, 9} and the relation R on A is defined by R = {(x, y) : x, y ∈ A, y = 2x + 1}, then determine whether the relation R is

(i) reflexive (ii) symmetric (iii) transitive

Sol :

Question 26

Let R be the relation on the set N given by R = {(a, b) : a = b – 2, b > 6}, then determine whether

(i) (2, 4) ∈ R

(ii) (6, 8) ∈ R

(iii) (9, 7) ∈ R.

Sol :

Question 27

If the relation R on the set N of natural numbers is defined by

R = {(a, b) : a, b ∈ N, a = 2b – 1, b > 4}, then determine whether

(i) (6, 11) ∈ R

(ii) (13, 7) ∈ R

(iii) (5, 3) ∈ R

Sol :

Question 28

If P be the set of people living in Delhi and R be the relation on P defined by

R = {(a, b) : a, b ∈ P, a lives within 4 km of b}, then determine whether R is transitive.

Sol :

Question 29

Is the relation R on the set R of real numbers defined by

R = {(a, b) : a, b ∈ R, 1 + ab ≥ 0} transitive? Justify your answer.

Sol :

Question 30

Is the relation R on the set Q of rational numbers defined by

$R = {(x, y) : x, y ∈ Q, x < y^2}$, symmetric? Justify your answer

Sol :

Question 31

If A = {1, 3, 7} and R be the relation ‘is greater than’ on the set A. Write R as a set of ordered pairs. Is this relation an equivalence relation?

Sol :

Question 32

If the relation R on the set A = {1, 2, 3} is defined by R = {(1, 1), (2, 2), (3, 3), (2 1), (3, 2)}, then determine whether the relation R is

(i) reflexive (ii) symmetric (iii) transitive

Sol :

Question 33

If R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}, then determine whether

(i) R is reflexive and symmetric but not transitive.

(ii) R is reflexive and transitive but not symmetric.

(iii) R is symmetric and transitive but not reflexive

Sol :

ML AGGARWAL CLASS 12 Chapter 6 Applications of derivative Exercise 6.2 (CBSE)

applied math 6.1 ml aggarwal class 12

Exercise 6.1

Question 1

Solve for x

(i) x(x-2)(x-5)(x+3)>0

Sol :

Here, x=0,2,5,3

Let's check sign's of intervals

-∞ and -3

Take any value between -∞ and -3

let say -10

and put it in x(x-2)(x-5)(x+3)

⇒-10(-10-2)(-10-5)(-10+3)

⇒-10(-12)(-15)(-7)

⇒12600

which means overall sign is (+ve) in interval -∞ and -3

In the same way, we going to find sign's for intervals

-3 and 0 (-ve)

0 and 2 (+ve)

2 and 5 (-ve)

5 and ∞ (+ve)

Since, the function is greater than 0, it include all positive intervals

So, x∈(-∞,-3)∪(0,2)∪(5,∞)

(ii) $x^{4}-5 x^{2}+4 \geqslant 0$

Sol :

Let $x^2=t$

$t^{2}-5 t+4 \geqslant 0$

$t^{2}-4 t-t+4 \geqslant 0$

(t-4)(t-1)≥0

$\left(x^{2}-4\right)\left(x^{2}-1\right) \geqslant 0$

(x-2)(x+2)(x-1)(x+1)≥0

So, x=2,-2,1-1

Since, the function is greater than 0, it include all positive intervals

x∈(-∞,-2]∪[-1,1]∪[2,∞)

Question 2

Find all real values of n :

(i) $x^{3}(x-1)(x-2)>0$

Sol :

Here , x=0,1,2

Since, the function is greater than 0, it include all positive intervals

Solution set : x∈(1,0)∪(2,∞)

(ii) $x^{2}(x-1)(x-2) \leq 0$

Sol :

Here, x=0,1,2

For (-∞,0) from inequality it is +ve

For (0,1) from inequality it is +ve

For (1,2) from inequality it is -ve

For (2,∞) from inequality it is +ve

Since, the function is less than 0, it include all negative intervals. Also, we include zero as well.

Solution set : x∈[1,2]∪{0}

Question 3

Solve for x

(i) $\frac{1}{x-2} \leq 1$

Sol :

$\frac{1}{x-2} \leq 1$ , x≠2

Multiplying both side by $(x-2)^{2}$

$(x-2)^{2} \times \frac{1}{(x-2)} \leq 1 \times(x-2)^{2}$

$(x-2) \leqslant x^{2}-4 x+4$

$0 \leq x^{2}-5 x+6$

$x^{2}-2x-3x+4 \geq 0$

(x-2)(x-3)≥0

Here, x=2,3

For (-∞,2) from inequality it is +ve

For (2,3) from inequality it is -ve

For (3,∞) from inequality it is +ve

Since, the function is greater than 0, it include all positive intervals

Solution set : x∈(-∞,2)∪[3,∞)

(ii) $\frac{(x+1)(x-3)}{(x+2)} \geqslant 0$

Sol :

$\frac{(x+1)(x-3)}{(x+2)} \geqslant 0$, x≠-2

Multiplying both side by (x+2)

(x+1)(x-3)(x+2)≥0

Here, x=-1,+3,-2

For (-∞,-2) from inequality it is -ve

For (-2,-1) from inequality it is +ve

For (-1,3) from inequality it is -ve

For (3,∞) from inequality it is +ve

Since, the function is greater than 0, it include all positive intervals

Solution set : x∈(-2,-1]∪[3,∞)

Question 1

ML AGGARWAL CLASS 10 Chapter 1 GST Chapter Test

Test

Page-19

OPEN IN YOUTUBE

Question 1

A shopkeeper bought a washing machine at a discount of 20% from a wholesaler the printed price the washing machine being *15000. The shopkeeper sells it to a consumer at a discount of 10% on the printed price. If the sales are intra-state and the

rate of GST is 12%, find:

(i) the price inclusive of tax (under GST) at which the shopkeeper bought the machine

(ii) the price which 1 the consumer pays for the machine.

(iii) the tax (under GST) paid by the wholesaler to the State Government

(iv) the tax (under GST) paid by the shopkeeper to the State Government

(v) the tax (under GST) received by the Central Government.

Sol :

Printed Price of the washing machine = ₹18000

Discount rate = 20 %

Discount = (20/100) x ₹18000

= ₹3600

So, the selling price of the washing machine = ₹18000 – ₹3600 = ₹14400

The rate of GST = 12%

The taxes (under GST) for the purchase are

SGST = ₹14400 x (12/2)/100 = ₹864

CGST = ₹14400 x (12/2)/100 = ₹864

(i) Hence, the shopkeeper bought the machine at the price = ₹14400 + ₹864 + ₹864 = ₹16128

(iii) The tax (under GST) paid by wholesaler to State Government = ₹864

The machine is sold to a consumer at 10% discount of the List /printed Price

Discount = (10/100) x ₹18000

= ₹1800

So, the selling price for the shopkeeper = ₹18000 – ₹1800 = ₹16200

The taxes (under GST) for the purchase are

SGST = ₹16200 x (12/2)/100 = ₹972

CGST = ₹16200 x (12/2)/100 = ₹972

(ii) Thus, the consumer paid a price = ₹16200 + ₹972 + ₹972 = ₹18144

(iv) The tax (under GST) paid by shopkeeper to State Government = ₹972 – ₹864 = ₹108

(v) The tax (under GST) received by the central Govt = ₹972

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Question 2

A manufacturer listed the price of his good at Rs 1600 per article He allowed a discount of 25% to a wholesaler who in turn allowed a discount of 20% on the listed price to a retailer The retailer sells one article to a at a discount of 5% on the listed Price. if all the sales are intra-state and the rate of GST is 5%, find;

(i) the price per article inclusive of tax (under GST) which the Wholesaler pays.

(ii) the price per article inclusive of tax (under GST) which the retailer pay

(iii) the amount which the consumer pays for the article.

(iv) the tax (under GST) paid by the whole to the State Government for the article

(v) the tax (under GST) paid by the retailer to the Central Government for the article,

(v) the tax (under GST) received by the State Government

Sol :

(i) The listed price per article = ₹1600

Discount rate from the manufacture = 25%

Discount = (25/100) x ₹1600 = ₹400

So, the selling price per article to the wholesaler = listed price – discount

= ₹1600 – ₹400

= ₹1200

The rate of GST = 5%

GST = 5% of ₹1200

= (5/100) x ₹1200

= ₹60

Thus, the price per article inclusive of tax (under GST) which the wholesaler pays = selling price of the manufacture + GST

= ₹1200 + ₹60

= ₹1260

(ii) The wholesaler resells at a discount of 20% on the listed price per article to the retailer

Discount = (20/100) x ₹1600

= ₹320

So, the selling price of the wholesaler = listed price – discount

= ₹1600 – ₹320

= ₹1280

The rate of GST = 5%

GST = 5% of ₹1280

= (5/100) x ₹1280

= ₹64

Thus, the price per article inclusive of tax (under GST) which the retailer pays = selling price of the wholesaler + GST

= ₹1280 + ₹64

= ₹1344

(iii) Further, the retailer resells at a discount of 5% on the listed per article to the consumer

Discount = (5/100) x ₹1600

= ₹80

So, the selling price of the wholesaler = listed price – discount

= ₹1600 – ₹80

= ₹1520

The rate of GST = 5%

GST = 5% of ₹1520

= (5/100) x ₹1520

= ₹76

Thus, the price per article inclusive of tax (under GST) which the consumer pays = selling price of the retailer + GST

= ₹1520 + ₹76

= ₹1596

(iv) The tax (under GST) paid by the wholesaler to the State Government for the article = ₹(64 – 62)/2

= ₹4/2

= 2

(v) The tax (under GST) paid by the retailer to the Central Government for the article = ₹ (76 – 84)/2

= ₹12/2

= ₹6

(vi) The tax (under GST) received by the State Government = ₹76/2 = ₹38

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Question 3

Mukerjee purchased a movie camera for Rs 25488 which includes 10%rebate on the list price and 18% tax (under GST) on the remaining Price. Find the marked price of the camera.

Sol :

Let the marked price of the camera = ₹100

Rebate of 10% = 10% discount = ₹10

Remaining (selling) price of the camera = ₹90

The rate of GST = 18%

So, tax (under GST) = 18% of ₹90 = ₹16.2

Total cost of the camera = Selling price + GST

= ₹90 + ₹16.2

= ₹106.20

Now,

Given purchase price = ₹25488

If purchase price is ₹106.20 then marked price is ₹100

So, if purchase price is ₹1 then marked price is ₹(100/ 106.20)

Thus, if purchase price is ₹25488 then marked price is

₹ {(100/106.20) x 25488} = ₹24000

Therefore, the marked price of the movie camera = ₹24000

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Question 4

The Marked Price of an article is Rs 7500 A shopkeeper buys the article from a wholesaler at some discount and sells t to a consumer at the marked price. The sales are intra-state and the rate of GST is 12%. lf the shopkeeper pays Rs 90 as tax (under GST)to the State Government find;

(i) the amount of discount

(ii) the price inclusive of tax (under GST) of the article which the shopkeeper paid

to the wholesaler.

Sol :

The marked price of the article = ₹7500

Let the discount be x%

Then, discount = (x/100) x ₹7500 = ₹75x

So, the selling price of the article from the wholesaler = ₹7500 – ₹75x

The rate of GST = 12%

The tax (under GST) paid by the shopkeeper to the State Government

= 6% of (₹7500 – ₹75x) … (i)

The shopkeeper resells the article at the marked price to a consumer

Then, the tax (under GST) paid by the shopkeeper to the State Government

= 6% of ₹7500 … (ii)

Hence, the net tax (under GST) paid by the shopkeeper to the State Government

= (ii) – (i)

= 6% of ₹75x

Given that the shopkeeper paid 90 as tax (under GST) to the State Government

So,

6% of ₹75x = ₹90

(6 × 75)x/100 = 90

x = (90 x 100)/(6 x 75)

x = 20

Thus, the discount is 20%

(i) Now, the amount of discount = 20% of 7500

= (20/100) x ₹7500

= ₹1500

(ii) The price inclusive of tax (under GST) of the article which the shopkeeper paid

to the wholesaler = (marked price – discount) + GST

GST = 12% of (marked price – discount)

= (12/100) x ₹(7500 – 1500)

= 0.12 x ₹6000

= ₹720

Therefore, the price inclusive of tax (under GST) of the article which the shopkeeper paid to the wholesaler = ₹6000 + ₹720 = ₹6720

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Question 5

A retailer buys an article at a discount of 15% on the printed price front a wholesaler. He marks up the price by 10% on the printed price but due to competition in the mark. he allows a discount of 5% on the marked price to a buyer If the rate of GST is 12% and the buyer pays Rs. 468.16 for the article inclusive of tax (under GST). find

p>(i) the printed price of the article,

(ii) the profit Percentage of the retailer.

Sol :

(i) the printed price of the article,= …..

The retailer marks up the price by 10% on the printed price

So, the marked price by the retailer = ₹x + 10% of ₹x

= ₹x + ₹0.1x

= ₹1.1x

Due to competition the retailer allows discount of 5% on the marked price, then

The selling price of the article = ₹1.1x – discount

Discount = 5% of ₹1.1x

= ₹ (5/100) x 1.1x

= ₹0.055x

The rate of GST = 12%

The tax (under GST) for the purchase = 12% of the selling price set by the retailer

= 12% of ₹ (1.1x – 0.055x)

= ₹ (12/100) x (1.045x)

Thus, the price of the article inclusive of GST = ₹1.045x + ₹ (12/100) x (1.045x)

Given, buyer pays ₹468.16 for the article inclusive of tax (under GST)

So,

1.045x + (12/100) x (1.045x) = 468.16

1.045x + 0.1254x = 468.16

1.1704x = 468.16

x = 468.16/1.1704

x = ₹400

Therefore, the printed price of the article is ₹400

(ii) the profit Percentage of the retailer= ……

Buy at = 400 – 15% of ₹400 = ₹400 – ₹60 = ₹340

Sold at = (₹400 + 10% of ₹400) – 5% of (₹400 + 10% of ₹400)

= ₹(400 + 40) – [(5/100) x ₹400 + 40)]

= ₹440 – ₹ (0.05 x 440)

= ₹440 – ₹22

= ₹418

Therefore, profit = Selling price – cost price = ₹418 – ₹340 = ₹78

Therefore,

the profit percentage =

(78/340) x 100 = 22.94%

ML AGGARWAL CLASS 10 Chapter 1 GST MCQs

MCQs

Page-17

A retailer purchases a fan for Rs 1500 from a wholesaler and sells t to a consumer at 10%profit if the sales are intra-state and the rate of GST is 12%, then choose the correct answer from the given four options for questions 1 to 6:

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Question 1

The selling price of the fan by the retailer (excluding tax) is?

(a) Rs.1500

(b) Rs.1650

(c) Rs. 1848

(d) Rs. 1800

Sol :

Cost price of fan for retailer = ₹ 1500

Given profit% = 10%

∴ Selling price of fan by the retailer

= C.P. + 10% of C.P.

$=\left(1500+\frac{10}{100}\times 1500\right)=1650$

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Question 2

The selling price of the fan including tax (under GST) by retailer is?

(a) Rs.1650

(b) Rs.1800

(c) Rs.1848

(d) Rs.1830

Sol :

Given, GST (rate) = 12%

∴GST=12% of S.P

$=\left(\frac{12}{100}\times 1650\right)=198$

Thus, the required selling price of fan including tax by the retailer (under GST)

= S.P. + GST = ₹ (1650 + 198) = ₹ 1848

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Question 3

The tax (under GST) paid by the wholesaler to the Central Government is ?

(a)Rs 90

(b)Rs 9

(c)Rs 99

(d) Rs 180

Sol :

The tax (under GST) paid by wholesaler to Central Government

=6% of 1500

$=\left(\frac{6}{100}\times 1500\right)$

=90

[SGST – CGST = ½ × rate of GST – 6%]

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Question 4

The tax (under GST) paid by the retailer to the State Government ?

(a) Rs 99

(b) Rs 9

(c)Rs 18

(d)Rs 198
Sol :
Amount of input SGST of the retailer = 6% of ₹ 1500

$=\left(\frac{6}{100}\times 1500\right)$

=90

Since, the retailer sells the article to the consumer at 10% profit,

S.P of article $=\left(1500+\frac{10}{100}\times 1500\right)$

=1650

Amount of output SGST of the retailer=6% of 1650

$=\left(\frac{6}{100}\times 1650\right)$

=99

Amount of tax (under GST) paid by retailer to State Government = Output SGST – Input SGST

= (99 – 9) = ₹9

Page-18

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Question 5

The tax (under GST) received by the Central Government is ?

(a)Rs 18

(b) Rs 198

(c) Rs 90

(d)Rs 99

Sol :

Amount of CGST paid by the retailer = Output CGST – Input CGST

= ₹ (99-90) = ₹9

Thus, amount of tax (under GST) received by Central Government

= CGST paid by distributor + CGST paid by retailer

= (6% of ₹1500) + 9

= 90 + 9 = ₹99

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Question 6

The cost of the fan to the consumer inclusive of tax is ?

(a)Rs 1650

(b) Rs 1800

(c)Rs 1830

(4) Rs 1848

Sol :

Here, selling price of fan = ₹1650

GST on fan = 12% of ₹1650

$=\left(\frac{12}{100}\times 1650\right)$

=198

Thus, cost of a fan to the consumer inclusive of tax

= ₹ (1650+198) = ₹1848

A shopkeeper bought a TV from a distributor at a discount of 25% of the listed price of Rs 32000. The shopkeeper sells the TV to a consumer at the listed price. if the sales are intra-state and the rate of GST la 18%, then choose the correct er from the given four options for questions 7 to 11:

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Question 7

The selling price of the TV including tax (under GST?) by the distributor is?

(a) Rs 32000

(b) Rs 24000

(c) Rs 28320

(4) Rs 26160

Sol :

It is case of intra state

Discount = 32000 x 25/100

= 8000

SP= 32000-8000

=24000

SP with GST by distributor

24000 + 24000 x 18/100

=28320

Hence option (c) is correct

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Question 8

The tax (under GST) paid by the distributor to the State Government is

(a) Rs 4320

(b) Rs 2160

(c) Rs 2880

(d) Rs 720

Sol :

Tax (under GST) paid by distributor to the State Government

= SGST = 9% of ₹24000

$=\left(\frac{9}{100}\times 24000\right)$

=2160

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Question 9

The tax (under GST) paid by the shopkeeper to the Central Government is?

(a)Rs 720

(b)Rs 1440

(c) Rs 2880

(4)Rs 2160

Sol :

Amount of input CGST by the shopkeeper,

CGST = ₹2160, SGST = ₹2160

Amount of GST collected by the shopkeeper or paid by the consumer

= 18% of ₹32000

$=\left(\frac{18}{100}\times 32000\right)$=5760

SGST = 5760/2 = ₹2880 = CGST

Amount of CGST paid by shopkeeper to Central Government = Output CGST – Input CGST

= 2880-2160 = ₹720

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Question 10

The tax (under GST) received by the State Government is?

(a)Rs 5760

(b) Rs 4320

(c) Rs 1440

(d) Rs 2880

Sol :

Amount of SGST paid by Shopkeeper to state government = ₹ 720

∴ Total tax (under GST) received by State Government = ₹2160 +₹720 = ₹2880

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Question 11

The price including tax (under GST) of the TV paid by the consumer is

(a)Rs 28320

(b) Rs 37760

(c) Rs 34880

(4) Rs 32000

Sol :

Consumer buy on list price 32000

It is a case of intra-state transaction of goods and services.

SGST = CGST = ½ GST

Given:

The price inclusive of tax (under GST) which the consumer pays for the TV.

CP of an article for shopkeeper = ₹32000

SP of article = ₹32000 + 18% of ₹32000

= ₹32000 + (18/100) × 32000

= ₹32000 + 5760

= 37760

Hence option (b) is correct

ML AGGARWAL CLASS 10 Chapter 1 GST Exercise 1

Exercise 1

Page-15

Q1 | Ex-1 | Class 10 | GST | Chapter 1 | ML Aggarwal | myhelper

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Question 1

An article is marked at * 15000. A dealer sells it to a consumer at 10% profit. If the rate of GST is 12%, find:

(i) the selling price (excluding tax) of the article.
(ii) the amount of tax (under GST) paid by the consumer.
(iii) the total amount paid by the consumer

Sol :

(i) the selling price (excluding tax) of the article.

15000+(15000×10)/100

150000+1500

16500

(ii) the amount of tax (under GST) paid by the consumer.

(16500×12) / 100

1980

(iii) the total amount paid by the consumer

16500+1980

18480

Q2 | Ex-1 | Class 10 | GST | Chapter 1 | ML Aggarwal | myhelper

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Question 2

A shopkeeper buy goods worth 4000 and sells these at a profit of 20% to a consumer in the same state. If GST is charged at 5%, find:

(i) the selling price (excluding tax) of the goods.
(ii) CGST paid by the consumer.
(iii) SGST paid by the consumer.
(iv) the total amount paid by the consumer.

Sol :

(i) the selling price (excluding tax) of the goods.

4000+4000×20/100

(ii) SGST paid by the consumer.

4800 x 2.5/100

120

(iv) the total amount paid by the consumer.

Amount = Selling price + CGST + SGST

4800 + 120 + 120

5040

Q3 | Ex-1 | Class 10 | GST | Chapter 1 | ML Aggarwal | myhelper

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Question 3

The marked price of an article is 12500. A dealer in Kolkata sells the article to consumer in the same city at a profit of 8%. If the rate of GST is 18%, find

(i) the selling price (excluding tax) of the article
(ii) IGST, CGST and SGST paid by the dealer to the Central and State Government
(iii) the amount which the consumer pays for the article.

Sol :

(i) the selling price (excluding tax) of the article

12500 + 12500 x 8/100

12500 + 1000

13500

(ii) IGST, CGST and SGST paid by the dealer to the Central and State Government

IGST, is nil due to intra state

CGST paid by the dealer to the Central Government

13500 x 9/100

1215

SGST paid by the dealer to the State Government

13500 x 9/100

1215

(iii) the amount which the consumer pays for the article.

Amount = Selling price + CGST + SGST

13500 + 1215 +1215

15930

Q4 | Ex-1 | Class 10 | GST | Chapter 1 | ML Aggarwal | myhelper

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Question 4

A shopkeeper buys an article from a wholesaler for 20000 and sells it to a consumer at 10% profit. If the rate of GST is 12%, find the tax liability of the shopkeeper.

Sol :

CP of article = 20000

Profit = 10% profit

rate of GST is 12%

to find the tax liability first find Selling Price

SP= CP+ Profit

SP = 20000 + 20000 x 10/100

=20000 + 2000

= 22000

now the tax liability= output CGST + SGST- input CGST + SGST

22000 x5/100 + 22000 x5/100

1100 + 1100

2200

Q5 | Ex-1 | Class 10 | GST | Chapter 1 | ML Aggarwal | myhelper

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Question 5

A dealer buys an article for 6000 from a wholesaler. The dealer sells the article consumer at 15% profit. If the sales are intra-state and the rate of GST is 18%, find

(i) input CGST and input SGST paid by the dealer.
(ii) output CGST and output SGST collected by the dealer.
(iii) the net CGST and SGST paid by the dealer.
(iv) the total amount paid by the consumer.

Sol :

(i) input CGST and input SGST paid by the dealer.

input CGST 6000 x 9/100 and input SGST 6000 x 9/100

540 and 540

(ii) first find SP

CP + Profit

6000 + 6000 x15/100

6000 +900

6900

output CGST 6900 x 9/100 and output SGST 6900 x 9/100

621 +621

1242

(iii) the net CGST paid by the dealer.

net CGST paid by the dealer. = output CGST – input CGST

= 621-540

= 81

net SGST paid by the dealer.

net SGST paid by the dealer. = output SGST – input SGST

= 621-540

= 81

(iv) the total amount paid by the consumer.

SP + SGST + CGST

6900 +81+81

7062

Q6 | Ex-1 | Class 10 | GST | Chapter 1 | ML Aggarwal | myhelper

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Question 6

A manufacturer buys raw material worth 7500 paying GST at the rate of 5%. He sell the finished product to a dealer at 40% profit. If the purchase and the sale both are intra-state and the rate of GST for the finished product is 12%, find:

(i) the input tax (under GST) paid by the manufacturer
(ii) the output tax (under GST) collected by the manufacturer
(iii) the tax (under CST) paid by the manufacturer to the Central and State Governments.
(iv) the amount paid by the dealer for the finished product.

Sol :

(i)

SP = 7500+7500 x40/100

SP = 7500+3000

SP=10500

the input tax (under GST) paid by the manufacturer

CGST= 7500 x2.5/100

=187.5

SGST=7500 x 2.5/100

=187.5

(ii) the output tax (under GST) collected by the manufacturer

CGST = 10500 x 6 /100

=630

SGST = 10500 x 6 /100

=630

(iii) the tax (under CST) paid by the manufacturer to the Central Governments.

CGST = output tax – input tax

CGST = 10500 x6 /100 – 7500 x 2.5/100

= 630-187.5

=442.50

SGST = output tax – input tax

SGST = 10500 x6 /100 – 7500 x 2.5/100

= 630-187.5

=442.50

(iv) the amount paid by the dealer for the finished product.

= SP+ Tax

=10500 + 10500 x12/100

=10500 + 1260

=11760

Page-16

Q7 | Ex-1 | Class 10 | GST | Chapter 1 | ML Aggarwal | myhelper

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Question 7

A manufacturer sells a TV. to a dealer for 18000 and the dealer sell it to a consumer at a profit of R1500. If the sales are intra-state and the rate of GST is 12%, find:

(i) the amount of GST paid by the dealer to the State Government
(ii) the amount of GST received by the Central Government
(iii) the amount of GST received by the State Government
T.V.
(iv) the amount that the consumer pays for the TV

Sol :

It is a case of intra-state

SGST = CGST = ½ GST

Given:

Manufacturer sells T.V to a dealer = ₹ 18000

Amount of GST collected by manufacturer from dealer,

CGST – SGST = 6% of 18000

= (6/100) × 18000

= ₹ 1080

So, Manufacturer will pay ₹ 1080 as CGST and ₹ 1080 as SGST

CP of a TV for dealer = ₹ 18000

Profit = ₹ 1500

SP of a TV for dealer to customer – CP + Profit = ₹ 18000 + ₹ 1500

= ₹ 19500

Amount of GST collected by dealer from customer,

CGST = SGST = 6% of ₹ 19500

= (6/100) × 19500

= ₹ 1170

(i) Amount of GST paid by the dealer to the State Government.

₹ 1170 – ₹ 1080 = ₹ 90

(ii) Amount of GST received by the Central Government.

CGST paid by manufacturer + CGST paid by dealer = ₹ 1080 + ₹ 90

= ₹ 1170

(iii) Amount of GST received by the State Government.

SGST paid by manufacturer + SGST paid by dealer = ₹ 1080 + ₹ 90

= ₹ 1170

(iv) Amount that the consumer pays for the TV.

CP of TV + CGST paid by customer + SGST paid by customer

= ₹19500 + ₹1170 + ₹ 1170 = ₹ 21840

Q8 | Ex-1 | Class 10 | GST | Chapter 1 | ML Aggarwal | myhelper

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Question 8

A shopkeeper buys a camera at a discount of 20% from a wholesaler, the printed price of the camera being RS 1600. The shopkeeper sells it to a consumer at the printed price

If the sales are intra-state and the rate of GST is 12%, find:
(i) GST paid by the shopkeeper to the Central Government.
(ii) GST received by the Central Government.
(iii) GST received by the State Government
(iv) the amount at which the consumer bought the camera

Sol :

It is a case of intra-state

SGST = CGST = ½ GST

Given:

Printed price of a camera = ₹ 1600

Rate of discount = 20%

It is given that, rate of GST = 12%

Amount of GST paid by the shopkeeper to the wholesaler,

CGST = SGST = 6% of ₹1280

= (6/100) × 1280

= ₹76.80

(i) GST paid by the shopkeeper to the Central Government

CGST = SGST = 6% of ₹1600

= (6/100) × 1600

= ₹96

GST paid by the shopkeeper to the Central Government = ₹96 – ₹76.80 = ₹19.20

(ii) GST received by the Central Government.

CGST paid by wholesaler + CGST paid by shopkeeper = ₹76.80 + ₹19.20 = ₹96

(iii) GST received by the State Government.

SGST paid by wholesaler + SGST paid by shopkeeper = ₹76.80 + ₹19.20 = ₹96

(iv) The amount at which the consumer bought the camera.

Amount paid by consumer for camera = CP of camera + CGST paid by consumer + SGST paid by consumer = ₹1600 + ₹96 + ₹96 = ₹1792

Q9 | Ex-1 | Class 10 | GST | Chapter 1 | ML Aggarwal | myhelper

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Question 9

A dealer buys an article at a discount of 30% from the wholesaler, the marked price being 6000. The dealer sells it to a consumer at a discount of 10% on the marked price.

If the sales are intra-state and the rate of GST is 5%, find
(i) the amount paid by the consumer for the article.
(ii) the tax (under GST) paid by the dealer to the State Government.
(iii) the amount of tax (under GST) received by the Central Government

Sol :

Since , it is a case of intra – state transaction of good and service.

SGST=CGST=(1/2) GST;

Rate of GST=5%

Rate of discount given by the wholesaler = 30%

CP of an article for dealer = Marked price – Discount

= ₹6000 – 30% of ₹6000

= ₹6000 – (30/100) × 6000

= ₹6000 – 1800

= ₹4200

Amount of GST paid by dealer to wholesaler,

CGST = SGST = 2.5% of ₹4200

= (2.5/100) × 4200

= ₹105

(i) The amount paid by the consumer for the article.

SP of an article for consumer = Marked price – Discount

= ₹6000 – 10% of ₹6000

= ₹6000 – (10/100) × 6000

= ₹6000 – 600

= ₹5400

Amount of GST paid by consumer to dealer,

CGST = SGST = 2.5% of ₹5400

= (2.5/100) × 5400

= ₹135

Amount paid by consumer for article = CP of article for consumer + CGST paid by consumer + SGST paid by consumer = ₹5400 + ₹135 + ₹135 = ₹5670

(ii) The tax (under GST) paid by the dealer to the State Government.

₹135 – ₹105 = ₹30

(iii) The amount of tax (under GST) received by the Central Government.

CGST paid by wholesaler + CGST by dealer = ₹105 + ₹30 = ₹135

Q10 | Ex-1 | Class 10 | GST | Chapter 1 | ML Aggarwal | myhelper

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Question 10

The printed price of an article is 50000. The wholesaler allows a discount of 10% to a shopkeeper. The shopkeeper sells the article to a consumer at 4% above the marked price. If the sales are intra-state and the rate of GST is 18%, find:

(i) the amount inclusive of tax (under GST) which the shopkeeper pays for the article
(ii) the amount paid by the consumer for the article.
(iii) the amount of tax (under GST) paid by the shopkeeper to the Central Government
(iv) the amount of tax (under GST) received by the State Government.

Sol :

It is a case of intra-state

SGST = CGST = ½ GST

Given:

Marked price of an article = ₹50000

Rate of GST = 18%

(i) The amount inclusive of tax (under GST) which the shopkeeper pays for the articles.

Rate of discount given by the wholesaler = 10%

CP of an article for shopkeeper = Marked price – Discount

= ₹50000 – 10% of ₹50000

= ₹50000 – (10/100) × 50000

= ₹50000 – 5000

= ₹45000

Amount of GST paid by dealer to wholesaler,

CGST = SGST = 9% of ₹45000

= (9/100) × 45000

= ₹4050

Amount paid by shopkeeper for an article = CP of an article for shopkeeper + CGST paid by consumer + SGST paid by consumer = ₹45000 + ₹4050 + ₹4050 = ₹53100

(ii) The amount paid by the consumer for the article.

SP of an article for consumer = Marked price – Discount

= ₹50000 – 4% of ₹50000

= ₹50000 – (4/100) × 50000

= ₹50000 – 2000

= ₹48000

Amount of GST paid by consumer to dealer,

CGST = SGST = 9% of ₹48000

= (9/100) × 48000

= ₹4320

Amount paid by consumer for article = CP of article for consumer + CGST paid by consumer + SGST paid by consumer = ₹48000 + ₹4320 + ₹4320 = ₹56640

(iii) The amount of tax (under GST) paid by the shopkeeper to the Central Government.

₹4320 – ₹4050 = ₹270

(iv) The amount of tax (under GST) received by the State Government.

SGST paid by wholesaler + SGST paid by shopkeeper = ₹4050 + ₹270 = ₹4320

Q11 | Ex-1 | Class 10 | GST | Chapter 1 | ML Aggarwal | myhelper

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Question 11

A retailer buys a T.V. from a wholesaler for 40000. He marks the price of the TV 15% above his cost price and sells it to a consumer at 5% discount on the marked price. If the sales are intra-state and the rate of GST is 12%, find:

(i) the marked price of the TV.
(ii) the amount which the consumer pays for the TV,
(iii) the amount of tax (under GST) paid by the retailer to the Central Government.
(iv) the amount of tax (under GST) received by the State Government.

SGST = CGST = ½ GST

Given:

(i) The marked price of the TV.

It is given that, CP of TV for retailer = ₹40000

Marked price of TV = ₹40000 + 15% of 40000

= ₹40000 + (15/100) × 40000

= ₹40000 + 6000

= ₹46000

(ii) The amount which the consumer pays for the TV.

It is given that, Discount given by retailer = 5% of ₹46000

= (5/100) × 46000

= ₹2300

Amount paid by consumer without GST for TV = ₹46000 – ₹2300

= ₹43700

Rate of GST = 12%

Amount of GST paid by consumer = 12% of ₹43700

= (12/100) × 43700

= ₹5244

Amount which consumer pays for TV = ₹43700 + ₹5244 = ₹48944

(iii) The amount of tax (under GST) paid by the retailer to the Central Government.

CGST paid by shopkeeper = 6% of ₹40000

= (6/100) × 40000

= ₹2400

SGST paid by shopkeeper = 6% of ₹40000 = ₹2400

Shopkeeper sells the article to consumer = ₹43700

GST collected by shopkeeper = 12% of ₹43700

= (12/100) × 43700

= ₹5244

CGST of shopkeeper = SGST = 6% of ₹43700

= (6/100) × 43700

= ₹2622

The amount of tax (under GST) paid by the retailer to the Central Government =

₹2622 – ₹2400 = ₹222

(iv) The amount of tax (under GST) received by the State Government.

SGST paid by wholesaler + SGST paid by shopkeeper = ₹2400 + ₹222 = ₹2622

Q12 | Ex-1 | Class 10 | GST | Chapter 1 | ML Aggarwal | myhelper

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Question 12

A shopkeeper buys an article from a manufacturer for 12000 and marks up it price by 25%. The shopkeeper gives a discount of 10% on the marked up price and he gives further off-season discount of 5% on the balance to a customer of T.V. If the sales are

intra-state and the rate of GST is 12%, find:
(i) the price inclusive of tax (under GST) which the consumer pays for the T.V.
(ii) the amount of tax (under GST) paid by the shopkeeper to the State Government.
(iii) the amount of tax (under GST) received by the Central Government.

Sol :

It is a case of intra-state

Therefore SGST = CGST = ½ GST

Given:

(i) The price inclusive of tax (under GST) which the consumer pays for the TV.

CP of an article for shopkeeper = ₹12000

Marked price of article = ₹12000 + 25% of ₹12000

= ₹12000 + (25/100) × 12000

= ₹15000

Amount of discount given by shopkeeper = 10% of ₹15000

= (10/100) × 15000

= ₹1500

Again, shopkeeper gives off season discount of 5% on the balance = 5% of (15000 – 1500) = (5/100) × 13500

= ₹675

CP of TV for consumer = ₹13500 – ₹675 = ₹12825

Amount of GST paid by consumer = 12% of ₹12825

= (12/100) × 12825

= ₹1539

The price inclusive of tax (under GST) which the consumer pays for the TV = ₹12825 + ₹1539 = ₹14364

(ii) The amount of tax (under GST) paid by the shopkeeper to the Stale Government.

CGST = SGST = 6% of ₹12000

= (6/100) × 12000

= ₹720

GST paid by consumer to shopkeeper,

CGST = SGST = 6% of ₹12825

= (6/100) × 12825

= ₹769.50

The amount of tax (under GST) paid by the shopkeeper to the Stale Government =

₹769.50 – ₹720 = ₹49.50

(iii) The amount of tax (under CST) received by the Central Government.

CGST paid by manufacturer = ₹720

CGST paid by shopkeeper = ₹769.50 – ₹720 = ₹49.50

The amount of tax (under CST) received by the Central Government =

₹720 + ₹49.50 = ₹769.50

Page-17

Q13 | Ex-1 | Class 10 | GST | Chapter 1 | ML Aggarwal | myhelper

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Question 13

The printed price of an article is 40000. A wholesaler in Uttar Pradesh buys the article from manufacturer in Gujarat at a discount of 10% on the printed price. The wholesaler … the article to a retailer in Himachal at 5% above the printed price. If the rate of

GST on the article to 18%, find:

(i) the amount inclusive of tax (under GST) paid by the wholesaler for the article.
(ii) the amount inclusive of tax (under GST) paid by the retailer for the article.
(iii) the amount of tax (under GST) paid by the wholesaler to the Central Government.
(iv) the amount of tax (under GST) received by the Central Government.

Sol :

It is inter-state in both case sales from manufacturer to wholesaler and wholesaler to retailer.

Therefore, CGST = SGST = 0

GST = IGST

Given:

Printed price of an article = ₹40000

Discount given by manufacturer = 10% of ₹40000

= (10/100) × 40000

= ₹4000

CP of article for wholesaler = ₹40000 – ₹4000 = ₹36000

CP of article without tax for retailer = ₹40000 + 5% of ₹40000

= ₹40000 + (5/100) × 40000

= ₹42000

(i) The amount inclusive of tax (under GST) paid by the wholesaler for the article.

Amount of GST paid by wholesaler to manufacturer = 18% of ₹36000

= (18/100) × 36000

= ₹6480

The amount inclusive of tax (under GST) paid by the wholesaler for the article =

₹36000 + ₹6480 = ₹42480

(ii) The amount inclusive of tax (under GST) paid by the retailer for the article.

Amount of GST paid by retailer to wholesaler = 18% of ₹42000

= (18/100) × 42000

= ₹7560

The amount inclusive of tax (under GST) paid by the retailer for the article =

₹42000 + ₹7560 = ₹49560

(iii) The amount of tax (under GST) paid by the wholesaler to the Central Government.

Amount of GST paid by wholesaler to manufacturer = 18% of ₹36000

= (18/100) × 36000

= ₹6480

Amount of GST paid by retailer to wholesaler = 18% of ₹42000

= (18/100) × 42000

= ₹7560

The amount of tax (under GST) paid by the wholesaler to the Central Government =

₹7560 – ₹6480 = ₹1080

(iv) The amount of tax (under GST) received by the Central Government.

IGST paid by wholesaler to the Central Government = ₹1080

IGST paid by manufacturer = ₹6480

The amount of tax (under GST) received by the Central Government = ₹1080 + ₹6480

= ₹7560

Q14 | Ex-1 | Class 10 | GST | Chapter 1 | ML Aggarwal | myhelper

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Question 14

A dealer in Delhi buys an article for 16000 from a wholesaler in Delhi. He sells the Article to a consumer in Rajasthan at a profit of 25%. If the rate of GST is 5%, find.

(i)in the tax (under GST) paid by the wholesaler to Governments.
(ii) the tax (under GST) paid by the dealer to the Government
(iii) the amount which the consumer pay for the article.

=16000 + 4000

= 20000

(i) CGST paid by the wholesaler to Governments.

= Output tax – Input Tax

= 20000 x 2.5 /100 -1600 x 2.5/100

=400

SGST paid by the wholesaler to Governments.

= Output tax – Input Tax

= 20000 x 2.5 /100 -16000 x 2.5/100

=400

(ii) CGST paid by the wholesaler to Governments.

= Output tax – Input Tax

= 20000 x 2.5 /100 -16000 x 2.5/100

=200 IGST to central government

(iii) the amount which the consumer pay for the article.

= SP + Tax

= 20000 + 20000 x5/100

=21000

Q15 | Ex-1 | Class 10 | GST | Chapter 1 | ML Aggarwal | myhelper

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Question 15

A shopkeeper in Delhi buys an article at the printed price of 24000 from a wholesaler in Mumbai. The shopkeeper sells the article to a consumer in Delhi at a profit of 15% on the basic cost price. If the rate of GST is 12%, find:

(i) the price inclusive of tax (under G5T) at which the shopkeeper bought the article.
(ii) the amount which the consumer pays for the article.
(iii) the amount of tax (under GST) received by the State Government of Delhi
(iv) the amount of tax (under GST) received by the Central Government.

Sol :

(i) The price inclusive of tax (under GST) at which the wholesaler bought the article.

CP of an article for shopkeeper = ₹24000

Rate of GST = 12%

IGST collected by wholesaler from shopkeeper = 12% of ₹24000

= (12/100) × 24000

= ₹2880

The price inclusive of tax (under GST) at which the wholesaler bought the article =

CP of article for shopkeeper + IGST paid by shopkeeper to wholesaler = ₹24000 + ₹2880

= ₹26880

(ii) The amount which the consumer pays for the article.

CP of an article for shopkeeper = ₹24000

Profit on CP of article = 15% of CP

SP of an article by the shopkeeper to consumer = CP + Profit

= ₹24000 + 15% of ₹24000

= ₹24000 + (15/100) × 24000

= ₹24000 + 3600

= ₹27600

The amount which the consumer pays for the article = CP of article for consumer + CGST paid by the consumer + SGST paid by consumer =

₹27600 + 6% of ₹27600 + 6% of ₹27600 =

₹27600 + (6/100) × ₹27600 + (6/100) × ₹27600 = ₹27600 + ₹1656 + ₹1656

= ₹30912

(iii) The amount of tax (under GST) received by the State Government of Delhi.

Amount of IGST for shopkeeper = ₹2880

SP of an article to consumer = CP of article for shopkeeper + profit on basic CP

= ₹24000 + 15% of ₹24000

= ₹24000 + (15/100) × ₹24000

= ₹24000 + ₹3600

= ₹27600

As the shopkeeper sells an article to consumer in Delhi; so this sales is Intra-state sales.

Amount of GST collected by shopkeeper from consumer,

CGST = SGST = 6% of ₹27600

= (6/100) × ₹27600

= ₹1656

Amount of tax paid by shopkeeper to state govt. = ₹2880 – ₹1656 = ₹1224

The amount of tax (under GST) received by the State Government of Delhi =

₹1656 – ₹1224 = ₹432

(iv) The amount of tax (under GST) received by the Central Government.

The amount of tax (under GST) received by the Central Government = IGST received from wholesaler + CGST received from shopkeeper = ₹ 2880 + NIL = ₹ 2880

Q16 | Ex-1 | Class 10 | GST | Chapter 1 | ML Aggarwal | myhelper

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Question 16

A dealer in Maharashtra buys an article from a wholesaler in Maharashtra at a discount of 25%, the printed price of the article being * 20000. He sells the article to a consumer in Telengana at a discount of 10%, on the printed price. If the rate of GST is 12%,, find:

(i) the tax (under GST) paid by the wholesaler to Governments.
(ii) the tax (under GST) paid by the dealer to the Government
(iii) the amount which the consumer pays for the article.

Sol :

(i) the tax (under GST) paid by the wholesaler to Governments.

SGST paid by the wholesaler to Governments.

= 15000 x 6/100

=900 to Maharastra Govt

CGST paid by the wholesaler to Governments.

= 15000 x 6/100

=900 to Maharastra Govt

(ii) the tax (under GST) paid by the dealer to the Government

Now sells are inter state hence all tax to central govt

CGST = Output – Input

= 18000 x 12/100 – 15000 x 12/100

= 360 IGST to central Govt

(iii) the amount which the consumer pays for the article.

= SP of dealer + Tax

=18000 + 18000 x 12/100

=18000+ 2160

= 20160

Q17 | Ex-1 | Class 10 | GST | Chapter 1 | ML Aggarwal | myhelper

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Question 17

Kiran purchases an article for * 5310 which includes 10% rebate on the marked price and 18% tax (under GST) on the remaining price. Find the marked price of the article.

Sol :

Rate of GST = 18%

CP of an article = x – 10% of x

= x – (10/100)x

= 90x/100

= 9x/10

Amount of GST on CP of article = 18% of 9x/10

= (18/100) × 9x/10

Total CP of article = 9x/10 + [(18/100) × 9x/10] – 9x/10(1 + 18/100) – (118/100) × 9x/10

It is given that, CP of an article including tax = ₹5310

So,

(118/100) × 9x/10 = 5310

x = 5310 × (100/118) × (10/9)

= 5000

The required marked price of an article is ₹5000

Q18 | Ex-1 | Class 10 | GST | Chapter 1 | ML Aggarwal | myhelper

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Question 18

A shopkeeper buys an article whose list price is 8000 at some rate of discount from a wholesaler. He sells the article to a consumer at the list price. The sales are intra-state and the rate of GST is 18%. If the shopkeeper pay a tax (under GST) of 72 to the State Government, find the rate of discount at which he bought the article from the wholesaler.

Sol :

List of price of an article = ₹8000

Let the rate of discount given by wholesaler = x%

So,

Discount = x% of ₹8000

= (x/100) × ₹8000

= ₹80x

CP of an article for shopkeeper = ₹8000 – ₹80x

It is given that, CP of article for consumer = ₹8000

Since the sales are intra-state, rate of GST = 18%

CGST = SGST = 9%

Amount of GST paid by shopkeeper to wholesaler,

SGST = CGST = 9% of [₹8000 – ₹80x]

(9/100) × [₹8000 – ₹80x]

Amount of GST paid by consumer to shopkeeper,

= (9/100) × ₹8000

= ₹720

So, the tax paid by shopkeeper to state government = ₹720 – (9/100) × [₹8000 – ₹80x]

Also, tax paid by shopkeeper to state government = ₹72

₹72 – 720 – (9×80) (100 – x) / (100)

720 – 72 = (720/100) (100 – x)

648 = (72/10) (100 – x)

100 – x = (648×10)/72

100 – x = 90

x = 100 – 90

= 10

So rate of discount = 10%

ML AGGARWAL CLASS 8 CHAPTER 8 Simple and Compound Interest Exercise 8.1

Exercise 8.1

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Question 1

Find the simple interest on ₹4000 at 7.5% p.a. for 3 years 3 months. Also, find the amount.

Sol :

Principal (P)=4000

Rate of Interest $(R)=7.5 \%$

Time (T)=3years and 3 months

$\begin{aligned} 1 \operatorname{month}&=\frac{1}{12} \text { year } \\ 3 \text { months } =\frac{3}{12} \text { year } &=\frac{1}{4} \text { year } \\ \therefore \text { Time } &=3 \cdot \frac{1}{4} \text { years }=\frac{13}{4} \text { years } \end{aligned}$

Simple Interest $(I)=\frac{P\times R \times T}{100}$

$=\frac{4000 \times \frac{15}{2}\times \frac{13}{4}}{100}$

$=\frac{4000\times 15\times 13}{2\times 4\times 100}$

=5×15×13

=975

Amount = Principal + Interest

= 4000 + 975

Amount = 4975

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Question 2

What sum of money will yield ₹170.10 as simple interest in 2 years 3 months at 6% per annum?

Sol :
Given

Simple Interest (I) = 170 .10

Time (T) = 2 year and 3 month

$=2 \cdot \frac{3}{12}=2 \cdot \frac{1}{4}=\frac{9}{4}$ years

Rate (R)= 6%

$\begin{aligned} P &=\frac{I \times 100}{R \times T} \\ &=\frac{170.10 \times 100}{6 \times \frac{9}{4}} . \end{aligned}$

Principal = p = 1260

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Question 3

Find the rate of interest when ₹800 fetches ₹130 as a simple interest in 2 years 6 months.

Sol :

Given

principal = 800

simple interest (I) = 130

Time = 2 year and 6 months

Time = $2 \cdot \frac{6}{12}=2 \cdot \frac{1}{2}=\frac{5}{2}$ years

$\begin{aligned} R &=\frac{I \times 100}{P \times T} \\ &=\frac{130 \times 100}{800 \times \frac{5}{2}} \\ R &=6.5 \% \end{aligned}$

hence , the required rate of interest = 6.5%

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Question 4

Find the time when simple interest on ₹3.3 lakhs at 6.5% per annum is ₹75075.

Sol :

Given

principal (p) = 3.3 lakhs
P= 330000

Rate (R)=6.5 %

$\begin{aligned} \text { Simple Interest } &=75075\\ \text { Time }(T) &=\frac{I \times 100}{P \times R} \\ &=\frac{75075 \times 100}{330000 \times 6.5} \\ T &=3.5 \text { years } \end{aligned}$

Hence , the required time = 3 years and 6 months

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Question 5

Find the sum of money when

(i) simple interest at $7\frac{1}{4}$% p.a. for $2\frac{1}{2}$ years is ₹2356.25

(ii) the final amount is ₹ 11300 at 4% p.a. for 3 years 3 months.

Sol :

(i) simple interest (I) = 2356.25

$\begin{aligned}(T) &=2 . \frac{1}{2} \text { yeers } \\ T &=\frac{5}{2} \text { years } \\(R) &=7 \cdot \frac{1}{4} \% \\ R &=\frac{29}{4}\\ P=& \frac{I \times 100}{T \times R} \\=& \frac{2356.25 \times 100}{\frac{5}{2} \times \frac{29}{4}} \\ P &=13,000\end{aligned}$

Hence , the required principal is Rs 13000

(ii) Given

Rate (R) = 4 %

$\begin{aligned} \text { Time }(T) &=3 \text { years and } 3 \text { month } s \\ &=3 \cdot \frac{3}{12}=3 \cdot \frac{1}{4}=\frac{13}{4} \\ T &=\frac{13}{4} \text { years } \end{aligned}$

Final Amount =113001

Final Amount = Principal (P)+Simple interest (I)

$11300=P+\frac{P \times R \times T}{100}$

$11300=P\left(1+\frac{T R}{100}\right)$

$11300=P\left(1+\frac{\frac{13}{4} \times 4}{100}\right)$

$11300=P\left(\frac{113}{100}\right)$

$P=11300 \times \frac{100}{113}$

P=10,000

Hence , the required principal is 10 ,000

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Question 6

How long will it take a certain sum of money to triple itself at $13\frac{1}{3}$% per annum simple interest?

Sol :

Given

Interest rate (R) = $13 \frac{1}{3}=\frac{40}{3}$ %

Final amount = 3 $\times $principal (p)

$\begin{aligned} P+I &=3 P \\ I &=3 p-P \\ I &=2 P \\ \frac{P T R}{100} &=2 P \quad\left(\because I=\frac{P T R}{100}\right) \\ T &=\frac{200}{R} \\ T &=\frac{200}{\frac{40}{3}} \end{aligned}$

Times = T = 15 years

Hence , the required time to triple itself for given

Interest rate is 15 years.

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Question 7

At a certain rate of simple interest ₹4050 amounts to ₹4576.50 in 2 years. At the same rate of simple interest, how much would ₹1 lakh amount to in 3 years?

Sol :

Given

principal $\left(P_{1}\right)=4050$

Final Amount =4576.501

$\begin{aligned} \text { Prinupal }+\text { Simple Interest }&=4576.50 \\ 4050+I_{1} &=4576.50 \\ I_{1} &=526.50\end{aligned}$

Time =2 year

$I_{1}=\frac{P_{1} T_{1} R}{100}$

$526.50=\frac{4050 \times 2 \times R}{100}$

R=6.5 % per annum

Now we have to calculate simple interest for 1 lakh for 3 years at a rate of 65 % per annum

$\begin{aligned} I_{2} &=\frac{P_{2} T_{2} R}{100} \\ I_{2} &=\frac{1,001000 \times 3 \times 6.5}{100} \\ I_{2} &=19500\end{aligned}$

$\begin{aligned} \text { Total Amount } &=P_{2}+I_{2} \\ &=1,00,000+19,500\\ &=1,19,500\end{aligned}$

∴ Hence , the 1 lakh will amount Rs 1,19,500 for 3 years

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Question 8

What sum of money invested at 7.5% p.a. simple interest for 2 years produces twice as much interest as ₹9600 in 3 years 6 months at 10% p.a. simple interest?

Sol :
Let the money invested to be Rs p

Given

Principal $P_{1}=P$

Rate $R_{1}=7.5$

Time $T_{1}=2$ years

Let Interest $=I_{1}$

Principal $P_{2}=₹ 9600$

Rate $R_{2}=10$

Time =3 years and 6 months.

Time $T_{z}=3 \cdot \frac{1}{2}=\frac{7}{2}$ years

let Simple Interest $=I_{2}$

$\therefore \quad I_{1}=2 \times I_{2}$

$\frac{P_{1} T_{1} R_{1}}{100}=2 \times \frac{P_{2} T_{2} R_{2}}{100}$

$\frac{P \times 2 \times 7.5}{100}=\frac{2 \times 9600 \times \frac{7}{2} \times 10}{100}$

P = Rs 4,4800

= Rs 44,800

Hence the required sum of money is Rs 44,800