S.chand publication New Learning Composite mathematics solution of class 8 Chapter 10 Quadrilaterals Exercise 10D

 Exercise 10D

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Q1 | Ex-10D | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

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Question 1

Find the measures of the numbered angles in each rectangle.

(a)

∠ABD=58°

∵AB⊥BC

DC⊥BC

AB=DC , AD=BC

AB||DC , AD||DC

∴∠ABC=90°

∴∠DBC=∠4=90°-58°=32°

∠DCB=∠3=90°=∠BAD

∴∠BAD=∠5=90°

∠ABC=∠ADC=90°

∴∠BDA=∠1=∠DBC=32°

Again, ∠ABD=∠BDC=∠2=58°

∴∠1=32°  ,∠3=90°

∠2=58° ,∠4=32°

∠5=90°

(b)

∵AD=DC=BC=AB

∠ADC=∠ABC=∠BAD=∠DCB=90°

∴∠1=∠ABC=90°

AC and BD bisect each other at O

∴∠ABD=∠DBC$=\frac{90}{2}$=45°

∴∠4=∠BDC=45°

∠BCA=∠5$=\frac{90}{2}$=45°

∴∠3=∠DAC=∠BCA=45°

∴∠CAB=∠2=45°

∴∠1=90° ,∠2=45° ,∠3=45° ,∠4=45°,∠5=45°

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Q2 | Ex-10D | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

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Question 2

In rectangle PQRS , S R=20 cm and PR=35 cm. Find:

(a) PQ  

(b) SK

PQRS is rectangle

SR=20 , PR=35

(a) PQ=20=SR  [∵SR=PS]

(b) ∵PR=SQ=35 [∵SR and PQ bisect each other at O]

∴$SQ=\frac{1}{2}$SK$=\frac{35}{2}$=17.5cm

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Q3 | Ex-10D | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

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Question 3

Find the value of each variable in these rectangles. Give brief reasons.

Sol :

(a) 

∵ABCD is a rectangle

∴AD=BC=x=7

AB=DC=y=4

∠a=90°=∠c  [∵AD⊥DC]

∠b=90°=∠d  [BC⊥DC]

(b)

AB=DC

AD=BC

∠BCD=90°

∴∠BCA=55°

∴∠ACD=90°-55°=35°

∴AD||BC and AB||DC

∴∠ACD=∠CAB=35°=y

∴x=∠DAC=∠BCA=55°

∴x=55°

and y=35°

(c) 

∵ABCD is rectangle

∴AB=DC  ∴AB⊥AD

AD=BC   DC⊥AD

∴∠ADC=5x=90°

∴$x=\frac{90}{5}$=18°

∴∠ADC=18°×5=90°

Now , 5y=15

∴$y=\frac{15}{5}=3$

∴AD=5×3=15

x=18 and y=3

(d)

AC and BD are bisect each other at "O"point

∴AC=BD

AD=BC   [AD||BC]

AB=DC  [AB||DC]

∴a=b=c=7unit

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Q4 | Ex-10D | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

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Question 4

Find the value of each variable in these rhombuses. Give brief reasons.

Sol :

(a)

ABCD is rhombus

∴AB||DC
AD||BC

∴AB=DC=AD=BC=x=9

AC and BD are intersection at the point "O"

∴AC=BD

∴AC⊥OD

AC⊥OB

∴∠BOC=a=∠AOB=90°

∴a=90° , x=9 unit ,y=9 unit

(b)

∵ABCD is rhombus

∴AD||BC

AB||DC

∴AD=BC , AB=DC

∴∠a=∠c=x

∠A=∠d=105°

In quadrilateral ABCD

∠A+∠a+∠c+∠d=360°

105°+x+x+105°=360°

210°+2x=360°

2x=360°-210°

$x=\dfrac{150^{\circ}}{2}$

x=75°

(c)

ABCD is rhombus

∵AC and BO are intersecting at point "O"

∴AO=OC=x=4

∴BO=OD=y=6

(d)

∠a=∠b=∠c=d

ΔABC

$2a+c+\frac{a}{2}=180^{\circ}$

$2a+\frac{a}{2}+\frac{a}{2}=180^{\circ}$  

[∵AB=BC

∴∠BAC=∠BCA

∴$\frac{a}{2}=C$]

$2a+\frac{2a}{2}=180^{\circ}$

3a=180°

$a=\frac{180}{3}$=60°

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Q5 | Ex-10D | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

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Question 5

In the rhombus ABCD, find

(a) BC

∵ABCD is a rhombus

∴AB=BC=AD=DC=4a+5=15a-6

∴We know

4a+5=15a-6

11a=11

a=1

∴BC=4a+5=4×1+5=9

(b) ∠BCO

AC and BD are intersecting at point "O"

∴∠BOC=90°

∴11b+2=90°

11b=90°-2°=88°

$b=\frac{88}{11}$=8

∴∠ACD=4b-10

=(4×8-10)

=32-10=22

∠ACD=∠BCO (Diagonals of rhombus bisect interior angles)

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Q6 | Ex-10D | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

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Question 6

Find the measures of the numbered angles in each rhombus.

(a)

Sol :

∠5=28° (Diagonals of rhombus bisect interior angle)

∠2=∠5=28° (alternate interior angle)

∠3=28° (alternate interior angle)

In triangle 

∠1+∠2+28°=180° (Angle sum property of triangle)

∠1+28°+28°=180°

∠1+28°+28°=180°

∠1+56°=180°

∠1=180°-56°=124°

∠1=∠4 (Opposite angle of rhombus are equal)

(b)

Sol :

∠A=50°, ∠B=∠2+∠3, ∠C=∠4, ∠D=∠1+∠5

∠4=50°...(i) (Opposite angle of rhombus are equal) 

∠B=∠D...(ii) (Opposite angle of rhombus are equal) 

In quadrilateral ABCD,

∠A+∠B+∠C+∠D=360° (Angle sum property of quadrilateral)

50°+∠B+∠B+50°=360° from (i) and (ii)

2∠B=360°-100°

2∠B=260°

$\angle B=\dfrac{260^{\circ}}{2}$

B=130°

∠2=∠3 and ∠1=∠5 (Diagonals bisect interior angle)

∠B=∠2+∠3

∠B=∠2+∠2

∠B=130°

∠2+∠2=130°

2∠2=130°

$\angle 2=\dfrac{130^{\circ}}{2}$

∠2=65°

∴∠1=∠2=∠3=∠5=65°

(c)

Sol :

∠3=28° (alternate interior angle)

∠4=90° (Diagonals of rhombus is perpendicular bisectors)

In triangle AOB ,

∠OAB+∠AOB+∠ABO=180°

∠3+∠4+∠ABO=180°

28°+90°+∠ABO=180°

118°+∠ABO=180°

∠ABO=62°

∠ABO=∠OBD=62° (Diagonals of rhombus bisect interior angle)

∠2=∠5=ABO=∠1=62° (alternate interior angle)

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Q7 | Ex-10D | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

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Question 7

Find the value of each variable in these squares. Give brief reasons.

(a)

ABCD is a square

∴AD=DC=BC=AB=x=y=6

∴∠BAD=∠ADC=∠DCB=∠CBA=a=b=c=d=90°

∴x=6 ,y=6   also, a=b=c=d=90°

(b)

AC and BD are intersect each other

AC=BD

∴∠BOC=90°

∴2p=90°

∴p=45°

Now ,ΔAOD

OD=OA [∴∠OAD=∠ODA=q]

∠AOD=90°

We know that

∠AOD+∠DOA+∠ODA=180°

90°+2q=180°

2q=180°-90°

2q=90°

$q=\frac{90}{2}$=45°

(c)

ABCD is square

AD=DC=BC=AB

AB and DC are intersecting at a point "O"

∴AO=OC=BO=OD=x=y=z=4

∴x=y=z=4

(d)

ABCD is square

∴AB=BC=DC=AD

∴∠ABC=∠BCD=∠CDA=∠DAB=90°

∴2x=90°

∴x=45°

∠CDA=90°

∠BDC$=\frac{1}{2}$∠CDA$=\frac{90}{2}=45$°=5y

∴5y=45°

y=9

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Q8 | Ex-10D | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

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Question 8

One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus.

Sol :

ABCD is rhombus

∴AC and BD are two diagonals

∴ Let , AC=x

AB=BC=CD=AD

ATQ ,

AB=x

∴ABC is equilateral triangle

ΔABC

AB=BC=AD

∠BAC=∠BCA=∠ABC=60°

∠B=60° , ∠A=60°×2=120° , ∠D=60° ,∠C=60°×2=120°

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Q9 | Ex-10D | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

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Question 9

ABCD is a rectangle. E is he midpoint of AB. Prove that △DEC is an isosceles triangle.

Sol :

E is mid point of AB

∴AE=EB

DC=CE

ABCD is a rhombus

AD=BC

ΔDEC➝

DE=CE

∴ΔDEC is isosceles triangle

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Q10 | Ex-10D | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

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Question 10

PQRS is a rhombus with diagonals PR which is extended to a point T. Prove that TQ = TS.

Sol :

PQRS is a rhombus

∴PQ=SR

PS=QR

∴In ΔTRS

SR²+TR²=TS²

In ΔTRS

RQ²+TR²=TQ²

SR²+TR²=TQ²

∴We can write

TS²=TQ²

or TS=TQ

RS Aggarwal solution class 8 chapter 10 Profit and Loss Exercise 10D

Exercise 10D

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Q1 | Ex-10D | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 1:

Tick (✓) the correct answer:
Rajan buys a toy for Rs 75 and sells it for Rs 100. His gain per cent is
(a) 25%
(b) 20%
(c) $33\frac{1}{3}\%$
(d) $37\frac{1}{2}\%$

Answer 1:

$$\begin{gathered} \left(\mathrm{c}\right) 33\frac{1}{3}\% \\ \mathrm{SP}=\mathrm{Rs} 100 \\ \mathrm{Gain}=\mathrm{Rs} \left(100-75\right) \\ =\mathrm{Rs} 25 \\ \therefore \mathrm{Gain} \mathrm{percentage}=\left(\frac{\mathrm{gain}}{\mathrm{CP}}\times 100\right)\% \\ =\left(\frac{25}{75}\times 100\right)\% \\ =33\frac{1}{3}\% \end{gathered}$$

Q2 | Ex-10D | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 2:

Tick (✓) the correct answer:
A bat is bought for Rs 120 and sold for Rs 105. The loss per cent is
(a) 15%
(b) $12\frac{1}{2}\%$
(c) $16\frac{2}{3}\%$
(d) $14\frac{1}{5}\%$

Answer 2:

   $$\begin{gathered} \left(\mathrm{b}\right)12\frac{1}{2}\% \\ \mathrm{CP}=\mathrm{Rs} 120 \\ \mathrm{SP}=\mathrm{Rs} 105 \\ \mathrm{Loss}=\mathrm{Rs} \left(120-105\right) \\ =\mathrm{Rs} 15 \\ \therefore \mathrm{Loss} \mathrm{percentage}=\left(\frac{\mathrm{loss}}{\mathrm{CP}}\times 100\right) \\ =\left(\frac{15}{120}\times 100\right) \\ =12\frac{1}{2}\% \end{gathered}$$

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Question 3:

Tick (✓) the correct answer:
A bookseller sells a book for Rs 100, gaining Rs 20. His gain per cent is
(a) 20%
(b) 25%
(c) 22%
(d) none of these

Answer 3:

 $$\begin{gathered} \left(\mathrm{b}\right) 25\% \\ \mathrm{CP}=\mathrm{SP}-\mathrm{Gain} \\ =\mathrm{Rs} \left(100-20\right) \\ =\mathrm{Rs} 80 \\ \therefore \mathrm{Gain} \mathrm{percentage}=\left(\frac{\mathrm{gain}}{\mathrm{CP}}\times 100\right)\% \\ =\left(\frac{20}{80}\times 100\right)\% \\ =25\% \end{gathered}$$

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Question 4:

On selling an article for Rs 48, a shopkeeper loses 20%. In order to gain 20%, what would be the selling price?
(a) Rs 52
(b) Rs 56
(c) Rs 68
(d) Rs 72

Answer 4:

 $$\begin{gathered} \left(\mathrm{d}\right) \mathrm{Rs} 72 \\ \mathrm{SP}=\mathrm{Rs} 48 \\ \mathrm{Loss}=20\% \\ \mathrm{Now}, \mathrm{CP}=\frac{100}{100-\mathrm{loss}\%}\times \mathrm{SP} \\ =\mathrm{Rs} \left(\frac{100}{\left(100-\mathrm{loss}\%\right)}\times \mathrm{SP}\right) \\ =\mathrm{Rs} \left(\frac{100}{\left(100-20\right)}\times 48\right) \\ =\mathrm{Rs} \left(\frac{100}{80}\times 48\right) \\ =\mathrm{Rs} 60 \end{gathered}$$

$\therefore \mathrm{Desired} \mathrm{SP}=\left\{\frac{\left(100+\mathrm{gain}\%\right)}{100}\times \mathrm{CP}\right\}$

                   $$\begin{gathered} =\left\{\frac{\left(100+20\right)}{100}\times 60\right\} \\ =\mathrm{Rs} \left(\frac{12}{10}\times 60\right) \\ =\mathrm{Rs} 72 \end{gathered}$$

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Question 5:

Tick (✓) the correct answer:
On selling an article at a certain price a man gains 10%. On selling the same article at double the price, gain per cent is
(a) 20%
(b) 100%
(c) 120%
(d) 140%

Answer 5:

(c) 120%

Let the SP and CP of the article be Rs x and y, respectively.
Gain percentage = 10%
⇒ 10 = $\frac{x-y}{y}\times 100$
⇒ y = $\frac{10x}{11}$

According to the question, we have:

SP = Rs 2x
∴ Gain percentage = $\frac{\mathrm{gain}}{\mathrm{CP}}\times 100$

                                $$\begin{gathered} =\frac{2x-{\displaystyle \frac{10x}{11}}}{{\displaystyle \frac{10x}{11}}}\times 100 \\ =\frac{12}{10}\times 100 \\ =120\% \end{gathered}$$

Q6 | Ex-10D | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 6:

Tick (✓) the correct answer:
Bananas are bought at 3 for Rs 2 and sold at 2 for Rs 3. The gain per cent is
(a) 25%
(b) 50%
(c) 75%
(d) 125%

Answer 6:

(d) 125%
$$\begin{gathered} \mathrm{Cost} \mathrm{price} \mathrm{of} \mathrm{a} \mathrm{banana}=\mathrm{Rs} \frac{2}{3} \\ \mathrm{Selling} \mathrm{price} \mathrm{of} \mathrm{a} \mathrm{banana}=\mathrm{Rs} \frac{3}{2} \\ \mathrm{Now}, \mathrm{profit} = \mathrm{Rs} (\frac{3}{2}-\frac{2}{3})=\mathrm{Rs} \frac{9-4}{6}=\mathrm{Rs} \frac{5}{6} \\ \therefore \mathrm{Gain} \mathrm{percentage} = \frac{\mathrm{gain}}{\mathrm{CP}}\times 100 \\ =\frac{\left({\displaystyle \frac{5}{6}}\right)}{\left({\displaystyle \frac{2}{3}}\right)}\times 100 \\ =\frac{5}{6}\times \frac{3}{2}\times 100 \\ = \frac{5}{4}\times 100 \\ =5\times 25 \\ =125\% \end{gathered}$$

Q7 | Ex-10D | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 7:

Tick (✓) the correct answer:
If the selling price of 10 pens is the same as the cost price of 12 pens then gain per cent is
(a) 2%
(b) 12%
(c) 20%
(d) 25%

Answer 7:

 (c) 20%    

$$\begin{gathered} \mathrm{Let} \mathrm{Rs} x \mathrm{be} \mathrm{the} \mathrm{SP} \mathrm{of} \mathrm{each} \mathrm{pen}. \\ \mathrm{SP} \mathrm{of} 10 \mathrm{pens}=\mathrm{CP} \mathrm{of} 12 \mathrm{pens}=\mathrm{Rs} 12x \\ \mathrm{CP} \mathrm{of} 10 \mathrm{pens}=\mathrm{Rs} 10x \\ \mathrm{Now}, \mathrm{gain}=\mathrm{Rs} \left(12\mathrm{x}-10\mathrm{x}\right) \\ =\mathrm{Rs} 2x \\ \therefore \mathrm{Gain} \mathrm{percentage}=\left(\frac{\mathrm{gain}}{\mathrm{CP}}\times 100\right)\% \end{gathered}$$
                            $$\begin{gathered} =\left(\frac{2x}{10x}\times 100\right)\% \\ =20\% \end{gathered}$$

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Question 8:

Tick (✓) the correct answer:
On selling 100 pencils a man gains the selling price of 20 pencils. His gain per cent is
(a) 20%
(b) 25%
(c) $22\frac{1}{2}\%$
(d) $16\frac{2}{3}\%$

Answer 8:

    (b) 25%

  $$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{SP} \mathrm{of} 100 \mathrm{pens} \mathrm{be} \mathrm{Rs} x. \\ \mathrm{SP} \mathrm{of} 1 \mathrm{pen}=\mathrm{Rs} \frac{x}{100} \\ \mathrm{Profit}=\mathrm{Rs} \frac{20x}{100} \\ =\mathrm{Rs} \frac{x}{5} \\ \mathrm{Now}, \mathrm{CP}=x-\frac{x}{5} \\ =\frac{4x}{5} \\ \therefore \mathrm{Gain} \mathrm{percentage}=\frac{{\displaystyle \frac{x}{5}}}{{\displaystyle \frac{4x}{5}}}\times 100 \\ =25\% \end{gathered}$$

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Question 9:

Tick (✓) the correct answer:
Ravi buys some toffees at 5 for a rupee and sells them at 2 for a rupee. His gain per cent is
(a) 30%
(b) 40%
(c) 50%
(d) 150%

Answer 9:

(d) 150%     

 ​ $$\begin{gathered} \mathrm{L}.\mathrm{C}.\mathrm{M} \mathrm{of} 5 \mathrm{and} 2=\left(5\times 1\times 2\right)=10 \\ \mathrm{Let} 10 \mathrm{be} \mathrm{the} \mathrm{number} \mathrm{of} \mathrm{toffees} \mathrm{bought}. \\ \mathrm{CP} \mathrm{of} 5 \mathrm{toffees}=\mathrm{Rs} 1 \\ \mathrm{CP} \mathrm{of} 1 \mathrm{toffee}=\mathrm{Rs} \left(\frac{1}{5}\right) \\ \therefore \mathrm{CP} \mathrm{of} 10 \mathrm{toffees}=\mathrm{Rs} \left(\frac{1}{5}\times 10\right) \\ =\mathrm{Rs} 2 \\ \mathrm{SP} \mathrm{of} 2 \mathrm{toffees}= \mathrm{Rs} 1 \\ \mathrm{SP} \mathrm{of} 1 \mathrm{toffee}=\mathrm{Rs} \left(\frac{1}{2}\right) \\ \therefore \mathrm{SP} \mathrm{of} 10 \mathrm{toffees}=\mathrm{Rs} \left(\frac{1}{2}\times 10\right) \end{gathered}$$
                                $=Rs.5$
  $$\begin{gathered} \mathrm{Gain}=\mathrm{Rs} \left(5-2\right) \\ =\mathrm{Rs} 3 \\ \mathrm{Gain} \mathrm{percentage}=\left(\frac{\mathrm{gain}}{\mathrm{CP}}\times 100\right)\% \\ =\left(\frac{3}{2}\times 100\right)\% \\ =150\% \end{gathered}$$

Q10 | Ex-10D | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 10:

Tick (✓) the correct answer:
Oranges are bought at 5 for Rs 10 and sold at 6 for Rs 15. His gain per cent is
(a) 50%
(b) 40%
(c) 35%
(d) 25%

Answer 10:

(d) 25%

  ​$$\begin{gathered} \mathrm{L}.\mathrm{C}.\mathrm{M} \mathrm{of} 5 \mathrm{and} 6=\left(5\times 1\times 6\right)=30 \\ \mathrm{Let} 30 \mathrm{be} \mathrm{the} \mathrm{number} \mathrm{of} \mathrm{oranges} \mathrm{bought}. \\ \mathrm{CP} \mathrm{of} 5 \mathrm{oranges}=\mathrm{Rs} 10 \\ \mathrm{CP} \mathrm{of} 1 \mathrm{oranges}=\mathrm{Rs} \left(\frac{10}{5}\right) \\ =\mathrm{Rs} 2 \\ \therefore \mathit{ }\mathrm{CP} \mathrm{of} 30 \mathrm{oranges}=\mathrm{Rs} \left(2\times 30\right) \\ =\mathrm{Rs} 60 \\ \mathrm{SP} \mathrm{of} 6 \mathrm{oranges}= \mathrm{Rs} 15 \\ \mathrm{SP} \mathrm{of} 1 \mathrm{oranges}=\mathrm{Rs} \left(\frac{15}{6}\right) \\ \therefore \mathrm{SP} \mathrm{of} 30 \mathrm{oranges}=\mathrm{Rs} \left(\frac{15}{6}\times 30\right) \end{gathered}$$

                                $=\mathrm{Rs} 75$

        $$\begin{gathered} \mathrm{Now}, \mathrm{gain}=\mathrm{Rs} \left(75-60\right) \\ =\mathrm{Rs} 15 \\ \therefore \mathrm{Gain} \mathrm{percentage}=\left(\frac{\mathrm{gain}}{\mathrm{CP}}\times 100\right)\% \\ =\left(\frac{15}{60}\times 100\right)\% \\ =25\% \end{gathered}$$

Q11 | Ex-10D | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 11:

Tick (✓) the correct answer:
By selling a radio for Rs 950, a man loses 5%. What per cent shall he gain by selling it for Rs 1040?
(a) 4%
(b) 4.5%
(c) 5%
(d) 9%

Answer 11:

​(a) 4%     

$$\begin{gathered} \mathrm{SP} \mathrm{of} \mathrm{the} \mathrm{radio}=\mathrm{Rs} 950 \\ \mathrm{Loss}=5\% \\ \mathrm{CP}=\left\{\frac{100}{\left(100-\mathrm{loss}\right)}\times \mathrm{SP}\right\} \\ =\mathrm{Rs} \left\{\frac{100}{\left(100-5\right)}\times 950\right\} \\ =\mathrm{Rs} \left(\frac{100}{95}\times 950\right) \\ =\mathrm{Rs} 1000 \end{gathered}$$
     
$$\begin{gathered} \mathrm{Now}, \mathrm{gain}=\mathrm{Rs} \left(1040-1000\right) \\ =\mathrm{Rs} 40 \\ \therefore \mathrm{Gain} \mathrm{percentage}=\left(\frac{\mathrm{gain}}{\mathrm{CP}}\times 100\right)\% \\ =\left(\frac{40}{1000}\times 100\right)\% \\ =4\% \end{gathered}$$

Q12 | Ex-10D | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 12:

Tick (✓) the correct answer:
The selling price of an article is $\frac{6}{5}$ of the cost price. The gain per cent is
(a) 20%
(b) 25%
(c) 30%
(d) 120%

Answer 12:

(a) 20%

 $$\begin{gathered} \mathrm{Let} \mathrm{Rs} x \mathrm{be} \mathrm{the} \mathrm{CP} \mathrm{of} \mathrm{each} \mathrm{article}. \\ \mathrm{SP} \mathrm{of} \mathrm{an} \mathrm{article}=\mathrm{Rs} \frac{6}{5}\mathrm{x} \\ \mathrm{Now}, \mathrm{gain}=\left(\mathrm{SP}-\mathrm{CP}\right) \\ =\mathrm{Rs} \left(\frac{6}{5}\mathrm{x}-\mathrm{x}\right) \\ =\mathrm{Rs} \frac{\mathrm{x}}{5} \\ \therefore \mathrm{Gain} \mathrm{percentage}=\left(\frac{\mathrm{gain}}{\mathrm{CP}}\times 100\right)\% \\ =\left(\frac{{\displaystyle \frac{\mathrm{x}}{5}}}{\mathrm{x}}\times 100\right)\% \\ =\left(\left(\frac{\mathrm{x}}{5}\times \frac{1}{\mathrm{x}}\right)\times 100\right)\% \\ =20\% \end{gathered}$$

Q13 | Ex-10D | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 13:

Tick (✓) the correct answer:
On selling a chair for Rs 720, a man loses 25%. To gain 25% it must be sold for
(a) Rs 900
(b) Rs 1200
(c) Rs 1080
(d) Rs 1440

Answer 13:

​ (b) Rs.1200     

$$\begin{gathered} \mathrm{SP}=\mathrm{Rs} 720 \\ \mathrm{Loss} \mathrm{percentage}=25\% \\ \mathrm{CP}=\left\{\frac{100}{\left(100-\mathrm{loss}\%\right)}\times \mathrm{SP}\right\} \\ =\mathrm{Rs} \left\{\frac{100}{\left(100-25\right)}\times \mathrm{SP}\right\} \\ =\mathrm{Rs} \left(\frac{100}{85}\times 720\right) \\ =\mathrm{Rs} 960 \\ \therefore \mathrm{Desired} \mathrm{SP}=\left\{\frac{\left(100+\mathrm{gain}\%\right)}{100}\times \mathrm{CP}\right\} \end{gathered}$$
                    $$\begin{gathered} =\mathrm{Rs}.\left\{\frac{\left(100+25\right)}{100}\times 960\right\} \\ =\mathrm{Rs}.\left(\frac{125}{100}\times 960\right) \\ =\mathrm{Rs}.1200 \end{gathered}$$

Q14 | Ex-10D | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 14:

Tick (✓) the correct answer:
The ratio of cost price and selling price of an article is 20 : 21. What is the gain per cent on it?
(a) 5%
(b) $5\frac{1}{2}\%$
(c) 6%
(d) $6\frac{1}{4}\%$

Answer 14:

(a) 5%
​

$$\begin{gathered} \mathrm{CP}=\mathrm{Rs}.20x \\ \mathrm{SP}=\mathrm{Rs}.21x \\ \mathrm{Gain}=\mathrm{Rs}.\left(21-20\right) \\ =\mathrm{Rs}.\mathrm{x} \\ \therefore \mathrm{Gain} \mathrm{percentage}=\left(\frac{\mathrm{gain}}{\mathrm{CP}}\times 100\right)\% \\ =\left(\frac{\mathrm{x}}{20\mathrm{x}}\times 100\right)\% \\ =5\% \end{gathered}$$

Q15 | Ex-10D | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 15:

Tick (✓) the correct answer:
A man sold two chairs for Rs 500 each. On one he gains 20% and on the other he loses 12%. His net gain or loss per cent is
(a) 1.5% gain
(b) 2% gain
(c) 1.5% loss
(d) 2% loss

Answer 15:

(a) 1.5% gain

​       $$\begin{gathered} \mathrm{SP} \mathrm{of} \mathrm{the} \mathrm{first} \mathrm{chair}=\mathrm{Rs} 500 \\ \mathrm{Gain} \mathrm{percentage}=20\% \\ \therefore \mathrm{CP} \mathrm{of} \mathrm{the} \mathrm{first} \mathrm{chair}=\left\{\frac{100}{\left(100+\mathrm{gain}\%\right)}\times \mathrm{SP}\right\} \end{gathered}$$
                                $$\begin{gathered} =\mathrm{Rs}.\left\{\frac{100}{\left(100+20\right)}\times 500\right\} \\ =\mathrm{Rs}.\left(\frac{100}{120}\times 500\right) \\ =\mathrm{Rs}.416.67 \end{gathered}$$
        
       $$\begin{gathered} \mathrm{SP} \mathrm{of} \mathrm{the} \mathrm{second} \mathrm{chair}=\mathrm{Rs}.500 \\ \mathrm{Loss} \mathrm{percentage}=12\% \\ \therefore \mathrm{CP} \mathrm{of} \mathrm{the} \mathrm{second} \mathrm{chair}=\left\{\frac{100}{\left(100-\mathrm{loss}\%\right)}\times \mathrm{SP}\right\} \end{gathered}$$
                                   $$\begin{gathered} =\mathrm{Rs}.\left\{\frac{100}{\left(100-12\right)}\times 500\right\} \\ =\mathrm{Rs}.\left(\frac{100}{88}\times 500\right) \\ =\mathrm{Rs}.568.18 \end{gathered}$$
   
  $\mathrm{Total} \mathrm{CP} \mathrm{of} \mathrm{the} \mathrm{two} \mathrm{chairs}=\mathrm{Rs}.\left(416.67+568.18\right)$
                                         $=Rs.984.85$
     $Total SP of the two chairs=Rs.\left(500\times 2\right)$
                                        $=Rs.1000$
      $$\begin{gathered} Since SP>CP, there is a gain in the whole transaction. \\ Now, gain=Rs.\left(1000-984.85\right) \\ =Rs.15.15 \\ \therefore Gain percentage=\left(\frac{gain}{CP}\times 100\right)\% \\ =\left(\frac{15.15}{984.85}\times 100\right)\% \\ =1.5\% \end{gathered}$$

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Q16 | Ex-10D | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 16:

Tick (✓) the correct answer:
The profit earned on selling an article for Rs 625 is the same as loss on selling it for Rs 435. The cost price of the article is
(a) Rs 520
(b) Rs 530
(c) Rs 540
(d) Rs 550

Answer 16:

(b) Rs 530    

 $$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{CP} \mathrm{be} \mathrm{Rs} x. \\ \mathrm{Then}, \mathrm{we} \mathrm{have}: \\ 625-x=\mathrm{x}-435 \\ \Rightarrow x+x=625+435 \\ \Rightarrow 2x=1060 \\ \therefore x= \mathrm{Rs} 530 \end{gathered}$$

Q17 | Ex-10D | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 17:

Tick (✓) the correct answer:
A man buys an article for Rs 150 and makes overhead expenses which are 10% of the cost price. At what price must he sell it to gain 20%?
(a) Rs 182
(b) Rs 192
(c) Rs 198
(d) Rs 208

Answer 17:

​(c) Rs 198  

    $$\begin{gathered} \mathrm{CP}=\mathrm{Rs} 150 \\ \mathrm{Total} \mathrm{CP}=\mathrm{Rs} \left(150+10\% \mathrm{of} 150\right) \\ =\mathrm{Rs} \left(150+\left(\frac{10}{100}\times 150\right)\right) \\ =\mathrm{Rs} \left(150+15\right) \\ =\mathrm{Rs} 165 \\ \therefore \mathrm{Desired} \mathrm{SP}=\left\{\frac{\left(100+\mathrm{gain}\%\right)}{100}\times \mathrm{total} \mathrm{CP}\right\} \end{gathered}$$
                     $$\begin{gathered} =\mathrm{Rs}.\left\{\frac{\left(100+20\right)}{100}\times 165\right\} \\ =\mathrm{Rs}.\left(\frac{120}{100}\times 165\right) \\ =\mathrm{Rs}.198 \end{gathered}$$

Q18 | Ex-10D | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 18:

Tick (✓) the correct answer:
If an article is sold at a gain of 5% instead of being sold at a loss of 5%, a man gets Rs 5 more. What is the cost price of the article?
(a) Rs 50
(b) Rs 40
(c) Rs 60
(d) Rs 80

Answer 18:

(a)​ Rs. 50     

 $$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{CP} \mathrm{be} \mathrm{Rs} x. \mathrm{Then}, \mathrm{we} \mathrm{have}: \\ \left(105\% \mathrm{of} \mathrm{x}\right)-\left(95\% \mathrm{of} \mathrm{x}\right)=5 \\ \Rightarrow \left(\frac{105}{100}\times \mathrm{x}\right)-\left(\frac{95}{100}\times \mathrm{x}\right)=5 \\ \Rightarrow \left(\frac{105\mathrm{x}}{100}-\frac{95\mathrm{x}}{100}\right)=5 \\ \Rightarrow \frac{\left(105\mathrm{x}-95\mathrm{x}\right)}{100}=5 \\ \Rightarrow \frac{10\mathrm{x}}{100}=5 \\ \Rightarrow \frac{\mathrm{x}}{10}=5 \\ \Rightarrow \mathrm{x}=50 \\ \therefore \mathrm{CP}=\mathrm{Rs} 50 \end{gathered}$$

Q19 | Ex-10D | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 19:

Tick (✓) the correct answer:
A dealer lists his articles at 20% above cost price and allows a discount of 10%. His gain per cent is
(a) 10%
(b) 8%
(c) 9 %
(d) $8\frac{1}{4}\%$

Answer 19:

​(b) 8%   

$$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{CP} \mathrm{be} \mathrm{Rs} 100. \\ \mathrm{Then}, \mathrm{marked} \mathrm{price}=\mathrm{Rs} 120 \\ \mathrm{Discount}=10\% \mathrm{of} \mathrm{MP}\mathrm{} \end{gathered}$$

            $$\begin{gathered} =\left(10\% \mathrm{of} \mathrm{Rs}120\right) \\ =\mathrm{Rs}.\left(120\times \frac{10}{100}\right) \\ =\mathrm{Rs}.12 \end{gathered}$$

 $$\begin{gathered} \mathrm{Now}, \mathrm{SP}=\left(\mathrm{MP}\right)-\left(\mathrm{discount}\right) \\ =\mathrm{Rs} \left(120-12\right) \\ =\mathrm{Rs} 108 \\ \mathrm{Gain} \mathrm{percentage}=\left(108-100\right)\% \\ =8\% \end{gathered}$$

Q20 | Ex-10D | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 20:

Tick (✓) the correct answer:
The marked price of an article is 10% more than the cost price and a discount of 10% is given on the marked price. The seller has
(a) no gain and no loss
(b) 1% gain
(c) 1% loss
(d) none of these

Answer 20:

​(c) 1% loss    

 $$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{CP} \mathrm{be} \mathrm{Rs} 100. \\ \mathrm{Then}, \mathrm{marked} \mathrm{price}=\mathrm{Rs} 110 \\ \mathrm{Discount}=10\% \mathrm{of} \mathrm{MP} \end{gathered}$$

      
             $$\begin{gathered} =\left(10\% \mathrm{of} \mathrm{Rs}.110\right) \\ =\mathrm{Rs}.\left(110\times \frac{10}{100}\right) \\ =\mathrm{Rs}.11 \end{gathered}$$

$$\begin{gathered} Now, SP=\left(MP\right)-\left(discount\right) \\ =Rs \left(110-11\right) \\ =Rs 99 \\ \therefore Loss percentage=(100-99)\%=1\% \end{gathered}$$
 

Q21 | Ex-10D | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 21:

Tick (✓) the correct answer:
The price of watch including 10% VAT is Rs 825. What is its basic price?
(a) Rs 742.52
(b) Rs 775
(c) Rs 750
(d) Rs 907.50

Answer 21:

(c) Rs.750

$$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{basic} \mathrm{price} \mathrm{be} x. \\ \mathrm{VAT}=10\% \mathrm{of} \mathrm{Rs} x \\ =\mathrm{Rs} \left(\mathrm{x}\times \frac{10}{100}\right) \\ =\mathrm{Rs} \frac{\mathrm{x}}{10} \\ \therefore \mathrm{Price} \mathrm{including} \mathrm{VAT}=\mathrm{Rs} \left(\mathrm{x}+\frac{\mathrm{x}}{10}\right) \end{gathered}$$
                                     $=Rs.\frac{11x}{10}$
$\mathrm{Now}, \frac{11\mathrm{x}}{10}=825$
    $$\begin{gathered} \Rightarrow x=\left(825\times \frac{10}{11}\right) \\ \Rightarrow x=750 \end{gathered}$$

∴ The basic price of the watch is Rs 750.