myhelper: Composite Maths

Showing posts with label Composite Maths. Show all posts

S.chand Class 8 Maths Solution Chapter 7 Linear Equations Exercise 7 B

Exercise 7 B

OPEN IN YOUTUBE

Question 1

The greater of two numbers is 12 more than the smaller and the sum of the two numbers is 10 . Find the numbers.

Sol :

OPEN IN YOUTUBE

Question 2

One number is 5 times another. If 18 is subtracted from the greater, the remainder will be 3 times the smaller. Find the numbers.

Sol :

OPEN IN YOUTUBE

Question 3

(i) Find three consecutive numbers whose sum is $108 .$

(ii) Find three consecutive odd numbers whose sum is $93 .$

(iii) Find three consecutive even numbers whose sum is $246 .$

(iv) The sum of three consecutive multiples of 7 is 777 . Find these multiples.

Sol :

OPEN IN YOUTUBE

Question 4

Divide 534 into three parts such that the second part will be 32 less than twice the first, and the third will be 18 more than the first.

Sol :

OPEN IN YOUTUBE

Question 5

Three times the smallest of three consecutive odd numbers decreased by 7 equals twice the largest one. Find the numbers.

Sol :

OPEN IN YOUTUBE

Question 6

One number is 7 more than another and its square is 77 more than the square of the smaller number. What are the numbers ?

Sol :

OPEN IN YOUTUBE

Question 7

The square of the greater of two consecutive even numbers exceeds the square of the smaller by 36 . Find the numbers.

Sol :

OPEN IN YOUTUBE

Question 8

The denominator of a fraction is 3 more than the numerator. If 5 is added to both parts, the resulting fraction is equivalent to $\frac{4}{5}$. Find the fraction.

Sol :

OPEN IN YOUTUBE

Question 9

The difference between two positive integers is 50 and the ratio of these integers is $1: 3$. Find these integers.

Sol :

OPEN IN YOUTUBE

Question 10

The sum of the digits of a two-digit number is 7 . The number obtained by interchanging the digits exceeds the original number by 27 . Find the number.

Sol :

OPEN IN YOUTUBE

Question 11

Sushma is now 15 years older than Vijay but in 3 more years she will be 8 times as old as Vijay was 3 years ago. How old are they now ?

Sol :

OPEN IN YOUTUBE

Question 12

Sanjay is now $\frac{1}{2}$ as old as his brother. In 6 more years he will be $\frac{3}{5}$ as old as his brother then. What is the present age of each boy ?

Sol :

OPEN IN YOUTUBE

Question 13

(a) If the area is $3 x \mathrm{~cm}^{2}$, make an equation, and find $x$.

(b) If the perimeter is 40 cm, make an equation, and find $x$.

Sol :

OPEN IN YOUTUBE

Question 14

$4(x-2)$ metres of rope is used to fence the rectangular enclosure shown in the Fig. Find x.

Sol :

OPEN IN YOUTUBE

Question 15

Madhu's flower garden is now a square. If she enlarges it by increasing the width 1 metre and the length 3 metres, the area will be 19 sq metres more than the present area. What is the length of a side ?

Sol :

OPEN IN YOUTUBE

Question 16

The sides (other than hypotenuse) of a right triangle are in the ratio 3: 4. A rectangle is described on its hypotenuse, the hypotenuse being the longer side of the rectangle. The breadth of the rectangle is four-fifth of its length. Find the shortest side of the right triangle, if the perimeter of the rectangle is 180 cm

Sol :

OPEN IN YOUTUBE

Question 17

Two cars leave Delhi at the same time, travelling in opposite directions. If the average speed of one car is $5 \mathrm{~km} / \mathrm{hr}$ more than that of the other and they are $425 \mathrm{~km}$ apart at the end of $5 \mathrm{hrs}$, what is the average speed of each?

Sol :

OPEN IN YOUTUBE

Question 18

Two automobiles start out at the same time from cities $595 \mathrm{~km}$ apart. If the speed of one is $\frac{8}{9}$ of the speed of the other and if they meet in 7 hours, what is the speed of each ?

Sol :

OPEN IN YOUTUBE

Question 19

A motorboat goes downstream in a river and covers the distance between two coastal towns in five hours. It covers this distance upstream in six hours. If the speed of the stream is $2 \mathrm{~km} / \mathrm{h}$, find the speed of the boat in still water.

Sol :

OPEN IN YOUTUBE

Question 20

A steamer, going downstream in a river, covers the distance between two towns in 20 hours. Coming back upstream, it covers this distance in 25 hours. The speed of water is $4 \mathrm{~km} / \mathrm{h}$. Find the distance between the two towns.

Sol :

OPEN IN YOUTUBE

Question 21

Ranjana's mother gave her $₹ 245$ for buying New Year cards. If she got some 10 -rupee cards, $\frac{2}{3}$ as many 5 rupee cards, and $\frac{1}{5}$ as many 15 -rupee cards, how many of each kind did she buy ?

Sol :

OPEN IN YOUTUBE

Question 22

The enrolment in a school this year is $552 .$ This is an increase of $15 \%$ over last year's enrolment. How many were enrolled last year?

Sol :

OPEN IN YOUTUBE

Question 23

A fruit vendor buys some oranges at the rate of $₹ 5$ per orange. He also buys an equal number of bananas at the rate of ₹ 2 per banana. He makes a $20 \%$ profit on oranges and a $15 \%$ profit on bananas. At the end of the day, all the fruit is sold out. His total profit is $₹ 390$. Find the number of oranges purchased.

Sol :

Multiple Choice Questions (MCQs)

OPEN IN YOUTUBE

Question 24

A two digit number becomes five-sixth of itself when its digits are reversed. The two digits differ by 1 . The number is

(a) 45

(b) 54

(c) 56

(d) 65

Sol :

OPEN IN YOUTUBE

Question 25

The ratio of the present ages of two brothers is $1: 2$ and 5 years back the ratio was $1: 3$. What will be the ratio of their ages after 5 years ?

(a) $1: 4$

(b) $2: 3$

(c) $3: 5$

(d) $5: 6$

Sol :

OPEN IN YOUTUBE

Question 26

Two trains start from $P$ and $Q$ respectively and travel towards each other at a speed of $50 \mathrm{~km} / \mathrm{hr}$ and $40 \mathrm{~km} / \mathrm{hr}$ respectively. By the time they meet, the first train has travelled $100 \mathrm{~km}$ more than the second. The distance between $P$ and $Q$ is

(a) $500 \mathrm{~km}$

(b) $630 \mathrm{~km}$

(c) $660 \mathrm{~km}$

(d) $900 \mathrm{~km}$

Sol :

High Order Thinking Skills (HOTS)

OPEN IN YOUTUBE

Question 27

Nine persons went to a hotel for taking their meals. Eight of them spent $₹ 12$ each over their meals and the ninth spent $₹ 8$ more than the average expenditure of all the nine. What was the total money spent by them ?

Sol :

S.chand Class 8 Composite Maths Solution Chapter 6 Factorisation of Algebraic Expressions Exercise 6 E

Exercise 6 E

Factorise the following expressions :

OPEN IN YOUTUBE

Question 1

$a^{2}-4$

Sol :

OPEN IN YOUTUBE

Question 2

$25-x^{2}$

Sol :

OPEN IN YOUTUBE

Question 3

$9 b^{2}-16$

Sol :

OPEN IN YOUTUBE

Question 4

$49 p^{2}-16$

Sol :

OPEN IN YOUTUBE

Question 5

$a^{2}-b^{2}$

Sol :

OPEN IN YOUTUBE

Question 6

$a^{2} x^{2}-y^{2}$

Sol :

OPEN IN YOUTUBE

Question 7

$49 c^{2}-25 d^{2}$

Sol :

OPEN IN YOUTUBE

Question 8

$100-r^{2}$

Sol :

OPEN IN YOUTUBE

Question 9

$49 a^{2}-1$

Sol :

OPEN IN YOUTUBE

Question 10

$100 b^{2}-81$

Sol :

OPEN IN YOUTUBE

Question 11

$x^{2} y^{2}-4$

Sol :

OPEN IN YOUTUBE

Question 12

$1-d^{2}$

Sol :

OPEN IN YOUTUBE

Question 13

$b^{4}-100$

Sol :

OPEN IN YOUTUBE

Question 14

$25-a^{2} x^{2} $

Sol :

OPEN IN YOUTUBE

Question 15

$144-a^{6}$

Sol :

OPEN IN YOUTUBE

Question 16

$b^{4}-a^{2}$

Sol :

OPEN IN YOUTUBE

Question 17

$a^{2} b^{2}-y^{2}$

Sol :

OPEN IN YOUTUBE

Question 18

$\frac{1}{4} b^{2}-49$

Sol :

OPEN IN YOUTUBE

Question 19

$c^{2}-0.36$

Sol :

OPEN IN YOUTUBE

Question 20

$x^{2}-\frac{1}{9}$

Sol :

OPEN IN YOUTUBE

Question 21

$\frac{4}{25} m^{2}-64$

Sol :

OPEN IN YOUTUBE

Question 22

$\frac{x^{2}}{9}-\frac{y^{2}}{4}$

Sol :

OPEN IN YOUTUBE

Question 23

$\frac{36}{a^{2}}-\frac{25}{b^{2}}$

Sol :

OPEN IN YOUTUBE

Question 24

$x^{2}-0.01$

Sol :

OPEN IN YOUTUBE

Question 25

$81-(x-7)^{2}$

Sol :

OPEN IN YOUTUBE

Question 26

$x^{3}-x$

Sol :

OPEN IN YOUTUBE

Question 27

$18 a^{2} x^{2}-32$

Sol :

OPEN IN YOUTUBE

Question 28

$3 x^{3} y-243 x y^{3}$

Sol :

OPEN IN YOUTUBE

Question 29

$a^{4}-81$

Sol :

OPEN IN YOUTUBE

Question 30

$x^{4}-y^{4}$

Sol :

OPEN IN YOUTUBE

Question 31

$a^{4}-16 x^{4} \quad$ 32. $x^{2}-y^{2}+2 x+1$

Sol :

OPEN IN YOUTUBE

Question 32

$x^{2}+4 y^{2}-z^{2}-4 x y$

Sol :

OPEN IN YOUTUBE

Question 33

$x^2+4y^2-z^2-4xy$

Sol :

Multiple Choice Questions (MCQs)

OPEN IN YOUTUBE

Question 34

$25(x+y)^{2}-36(x-2 y)^{2}$ can be factorised as :

(a) $(5 x-12 y)(-6 x+5 y)$

(b) $(11 x-7 y)(-x+17 y)$

(c) $(-11 x+7 y)(x-17 y)$

(d) $(-5 x+12 y)(6 x-5 y)$

Sol :

OPEN IN YOUTUBE

Question 35

One of the factors of $x^{2}+y^{2}+2 x y-z^{2}$ is

(a) $(x-y+z)$

(b) $(x+y-z)$

(c) $(-x-y+z)$

(d) $(-x+y-z)$

Sol :

High Order Thinking Skills (HOTS)

OPEN IN YOUTUBE

Question 36

Factorize $\left(256 x^{16}-1\right)$

Sol :

S.chand Class 8 Maths Solution Chapter 1 Rational Numbers Exercise 1B

Exercise 1B

OPEN IN YOUTUBE

Question 1

Answer True (T) or False (F) :

(i) Subtraction is commutative for rational numbers.

(ii) To subtract $\frac{c}{d}$ from $\frac{a}{b}$. We add the additive inverse of $\frac{a}{b}$ to $\frac{c}{d}$.

(iii) 0 is its own additive inverse.

(iv) The additive inverse of $\frac{-21}{-30}$ is $\frac{-21}{30}$.

(v) While subtracting three or more rational numbers, they can be grouped in any order.

Sol :

OPEN IN YOUTUBE

Question 2

Add the following rational numbers :

(i) $\frac{3}{7}$ and $\frac{2}{7}$

(ii) $-\frac{11}{13}$ and $\frac{9}{13}$

(iii) $\frac{-1}{6}$ and $\frac{3}{10}$

(iv) $\frac{-5}{12}$ and $\frac{-7}{18}$

(v) $\frac{6}{15}$ and $\frac{-7}{25}$

(vi) $\frac{13}{14}$ and $\frac{9}{-7}$

(vii) $3 \frac{3}{4}$ and $4 \frac{1}{3}$

(viii) $2 \frac{5}{7}$ and $\frac{-3}{-14}$

Sol :

OPEN IN YOUTUBE

Question 3

Simplify :

(i) $\frac{5}{6}+\frac{7}{18}+\frac{-11}{12}$

(ii) $\frac{7}{15}+\frac{-9}{25}+\frac{-3}{10}$

(iii) $\frac{-2}{3}+1 \frac{5}{6}+\frac{-3}{2}$

(iv) $4 \frac{1}{5}+\left(-5 \frac{3}{10}\right)+1 \frac{1}{2}$

Sol :

OPEN IN YOUTUBE

Question 4

Verify the following :

(i) $\frac{3}{4}+\frac{-2}{5}=\frac{-2}{5}+\frac{3}{4}$

(ii) $\frac{-3}{4}+\frac{7}{-8}=\frac{7}{-8}+\frac{-3}{4}$

(iii) $-8+\frac{-11}{-12}=\frac{-11}{-12}+(-8)$

OPEN IN YOUTUBE

Question 5

Verify that :

(i) $\left(\frac{-5}{8}+\frac{9}{8}\right)+\frac{13}{8}=\frac{-5}{8}+\left(\frac{9}{8}+\frac{13}{8}\right)$

(ii) $-20+\left(\frac{3}{-5}+\frac{-7}{-10}\right)=\left(-20+\frac{3}{-5}\right)+\frac{-7}{-10}$

Sol :

OPEN IN YOUTUBE

Question 6

Find the additive inverse of each of the following :

(i) $\frac{2}{3}$

(ii) 0

(iii) $\frac{17}{9}$

(iv) $\frac{-15}{-11}$

(v) -23

(vi) $\frac{-16}{13}$

(vii) $\frac{8}{-29}$

Sol :

OPEN IN YOUTUBE

Question 7

Arrange and simplify :

(i) $\frac{1}{2}+\frac{-3}{5}+\frac{3}{2}$

(ii) $\frac{28}{17}+\frac{35}{17}+\frac{-16}{17}+\frac{-23}{17}$

(iii) $\frac{2}{3}+\frac{-3}{5}+\frac{1}{6}+\frac{-8}{15}$

(iv) $\frac{3}{5}+\frac{5}{3}+\frac{-11}{5}+\frac{-2}{3}$

(v) $\frac{4}{3}+\frac{3}{5}+\frac{-2}{3}+\frac{-11}{5}$

(vi) $\frac{4}{9}+\frac{5}{3}+\frac{-4}{5}+\frac{7}{9}+\frac{-2}{3}+\frac{9}{5}$

Sol :

OPEN IN YOUTUBE

Question 8

Verify that -(-x)=x, when x= (a) $\frac{7}{6}$

(b) $\frac{-8}{9}$.

Sol :

OPEN IN YOUTUBE

Question 9

Verify that $-(x+y)=(-x)+(-y)$, when

(a) $x=\frac{3}{4}, y=\frac{6}{7}$

(b) $x=\frac{-3}{4}, y=\frac{-6}{7}$.

Sol :

OPEN IN YOUTUBE

Question 10

Subtract :

(i) $\frac{1}{5}$ from $\frac{3}{5}$

(ii) $\frac{4}{9}$ from $\frac{-1}{6}$

(iii) $\frac{-4}{15}$ from $\frac{3}{10}$

(iv) $\frac{3}{-4}$ from $\frac{4}{5}$

Sol :

OPEN IN YOUTUBE

Question 11

The sum of two rational numbers is $\frac{5}{18}$. If one of the numbers is $\frac{1}{8}$, find the other.

Sol :

OPEN IN YOUTUBE

Question 12

What number should be subtracted from $\frac{7}{-8}$ to get $\frac{-13}{12}$ ?

Sol :

OPEN IN YOUTUBE

Question 13

What should be subtracted from $\left(\frac{3}{4}+\frac{1}{3}+\frac{2}{5}\right)$ to get $\frac{1}{2}$ ?

Sol :

MULTIPLE CHOICE QUESTION (MCQS)

OPEN IN YOUTUBE

Question 14

What number should be added to $\frac{-5}{16}$ to get $\frac{7}{24}$ ?

(a) $\frac{-29}{48}$

(b) $\frac{15}{48}$

(c) $\frac{29}{48}$

(d) $\frac{21}{28}$

Sol :

OPEN IN YOUTUBE

Question 15

$\frac{-5}{7}+\frac{1}{12}+\frac{3}{4}+\frac{-1}{3}+\frac{10}{7}+-\frac{1}{6}$ equals

(a) 0

(b) 1

(c) $1 \frac{1}{21}$

(d) -1

Sol :

S.chand Composite Maths books class 8 maths solution chapter 28 Data Handling exercise 28 A

EXERCISE 28 A

Q1 | Ex-28A | Class 8 | SChand Composite Maths | Data Handling | myhelper

OPEN IN YOUTUBE

Question 1

Write (T) for true or (F) for false. Use the following frequency table.

Age	13	14	15	16	17	18	19
Frequency	3	2	7	2	3	2	1

(i) The frequency of 19 is 1

Sol : T

(ii) The frequency of 14 is 3

Sol : F

(iii) 17 has the lowest frequency

Sol : F

(iv) 16 has a frequency of 2

Sol : T

(v) 15 has the highest frequency

Sol : T

(vi) The frequency of 13 is 3

Sol : T

Q2 | Ex-28A | Class 8 | SChand Composite Maths | Data Handling | myhelper

OPEN IN YOUTUBE

Question 2

The ages of all the workers in a certain company are as follows:
23,28,25,21,40,50,50,21,40,50,33,28,41,25,33,37,23,26,41,37,37,21,43,33,37,28,32,33,43,32.
(i) Construct a frequency table for the above data.

Sol :

Ages	21	23	25	26	28	32	33	37	40	41	43	50
Frequency	3	2	2	1	3	2	4	4	2	2	2	3

(ii) How many workers are over 35 years old ?

Sol : 13

(iii) How many workers are under 30 years old ?

Sol : 11

(iv) What is the least age?

Sol : 21 years

Q3 | Ex-28A | Class 8 | SChand Composite Maths | Data Handling | myhelper

OPEN IN YOUTUBE

Question 3

Find the mean of the following sets of numbers.
(i)2.5,2.4,3.5,2.8,2.9,3.3,3.6

Sol :

$\overline{x}=\dfrac{2.5+2.4+3.5+2.8+2.9+3.3+3.6}{7}$

(ii)-6,-2,-1,0,1,2,5,9

Sol :

$\overline{x}=\dfrac{-6+(-2)+(-1)+0+1+2+5+9}{8}$

Q4 | Ex-28A | Class 8 | SChand Composite Maths | Data Handling | myhelper

OPEN IN YOUTUBE

Question 4

Anu received 85, 73, 92, 61 and 89 marks in five tests. What are her mean marks?

Sol :

$\overline{x}=\dfrac{85+73+92+61+89}{5}$

=80 marks

Q5 | Ex-28A | Class 8 | SChand Composite Maths | Data Handling | myhelper

OPEN IN YOUTUBE

Question 5

Priya practiced on her sitar 45 minutes, 30 minutes, 60 minutes, 50 minutes and 20 minutes. What was her mean practice time ?

Sol :

$\overline{x}=\dfrac{45+30+60+50+20}{5}$

$=\dfrac{205}{5}=41$ minutes

Q6 | Ex-28A | Class 8 | SChand Composite Maths | Data Handling | myhelper

OPEN IN YOUTUBE

Question 6

Find the mean of the first ten prime numbers.

Sol :

First ten prime numbers=2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

$\overline{x}=\dfrac{2+3+5+7+11+13+17+19+23+29}{10}$

$=\dfrac{129}{10}$=12.9

Q7 | Ex-28A | Class 8 | SChand Composite Maths | Data Handling | myhelper

OPEN IN YOUTUBE

Question 7

Shikha secured 73, 86, 78 and 75 marks in four tests. What is the least number of points she can secure in her next test if she is to have an average of 80?

Sol :

A.T.Q

Mean of 5 test is 80

Four test marks 73, 86, 78 and 75 and let the fifth test marks be x

∴$\dfrac{73+86+78+75+x}{5}=80$

312+x=80×5

x=400-312=88

∴88 marks will be required in 5th test.

Q8 | Ex-28A | Class 8 | SChand Composite Maths | Data Handling | myhelper

OPEN IN YOUTUBE

Question 8

The mean of 5 numbers is 20. if one number is excluded, mean of the remaining numbers becomes 23.Find the excluded number.

Sol :

Let the excluded number be x (5th number)

A.T.Q

Mean of 4 number is 23, which is equal to

$\dfrac{\text{Sum of 4 numbers}}{4}=23$

Sum of 4 numbers =23×4

Sum of 4 numbers =92...(i)

Mean of 5 numbers is 20, which is equal to

$\dfrac{\text{Sum of 4 numbers + 5th number }}{5}=20$

Sum of 4 numbers + x=20×5

Sum of 4 numbers + x=100

92+x=100 (From above)

x=100-92=8

Excluded number x= 8

Q9 | Ex-28A | Class 8 | SChand Composite Maths | Data Handling | myhelper

OPEN IN YOUTUBE

Question 9

Find the mean of the following distributions
(i)

x	4	6	9	10	15
f	5	10	10	7	8

Sol :

x	f	f.x
4	5	20
6	10	60
9	10	90
10	7	70
15	8	120
	𝝨f=40	𝝨f.x=360

$\overline{x}=\dfrac{\sum fx}{\sum f}=\frac{360}{40}$

(ii)

x	10	30	50	70	89
f	7	8	10	15	10

Sol :

x	f	f.x
10	7	70
30	8	240
50	10	500
70	15	1050
89	10	890
	𝝨f=50	𝝨f.x=2750

$\overline{x}=\dfrac{\sum fx}{\sum f}=\frac{2750}{50}$

=55

Q10 | Ex-28A | Class 8 | SChand Composite Maths | Data Handling | myhelper

OPEN IN YOUTUBE

Question 10

The following table gives the height in cm and the number of plants of each height. Compute the mean height of the plants.

Height in cm (x)	50	53	61	64	67	70
Number of plants (f)	15	10	18	12	25	20

Sol :

x	f	f.x
50	15	750
53	10	530
61	18	1098
64	12	768
67	25	1675
70	20	1400
	𝝨f=100	𝝨f.x=6221

$\overline{x}=\dfrac{\sum fx}{\sum f}=\frac{6221}{100}$

=62.21 cm