8th Maths 2.4

Chapter 2 Linear Equations in One Variable

NCERT Class 8th solution of Exercise 2.1

NCERT Class 8th solution of Exercise 2.2

NCERT Class 8th solution of Exercise 2.3

NCERT Class 8th solution of Exercise 2.5

NCERT Class 8th solution of Exercise 2.6

Exercise 2.4

Q1. Amina thinks of a number and subtracts

\frac{5}{2}

$5/2$ from it. She multiplies the result by

8

$8$ . The result now obtained is

3

$3$ times the same number she thought of. What is the number?

Sol.

$text{Sol.}$

Let Amina thinks of a number is x

$text{Let Amina thinks of a number is x}$

According to question

$text{According to question}$

(x - \frac{5}{2}) \times 8 = 3 \times x

$(text{x} - 5/2)times8 = 3 times text{x}$

8x - 20 = 3x

$text{8x - 20 = 3x}$

8x - 3x = 20

$text{8x - 3x = 20}$

5x = 20

$text{5x = 20}$

x = \frac{20}{5}

$text{x} = 20/5$

x = 4

$text{x} = 4$

Answer:

$text{Answer:}$

The number is 4.

$text{The number is 4.}$

Q2. A positive number is

5

$5$ times another number. If

21

$21$ is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers?

Sol.

$text{Sol.}$

Let a positive no. is x

$text{Let a positive no. is x}$

and another no. is 5x

$text{and another no. is 5x}$

According to question

$text{According to question}$

2(x +21) = 5x + 21

$text{2(x +21) = 5x + 21}$

2x + 42 = 5x + 21

$text{2x + 42 = 5x + 21}$

5x - 2x = 42 - 21

$text{5x - 2x = 42 - 21}$

3x = 21

$text{3x = 21}$

x = \frac{21}{3}

$text{x} = 21/3$

x = 7

$text{x} = 7$

5x = 7 \times 5 = 35

$text{5x} = 7times5 = 35$

Answer:

$text{Answer:}$

The numbers are 7 and 35.

$text{The numbers are 7 and 35.}$

Q3. Sum of the digits of a two-digit is

9

$9$ . When we interchange the digits, it is found that the resulting new number is greater than the original number by

27

$27$ . What is the two-digit number?

Sol.

$text{Sol.}$

Let tens digit is x

$text{Let tens digit is x}$

and ones digit is 9 - x

$text{and ones digit is 9 - x}$

original number 10x + (9 - x)

$text{original number 10x + (9 - x)}$ ____

(A)

$text{(A)$

According to question

$text{According to question}$

[10(9 - x) + x ]+ 27 = 10x + (9 - x)

$text{[10(9 - x) + x ]+ 27 = 10x + (9 - x)}$

90 - 10x + x + 27 = 10x + 9 - x

$text{90 - 10x + x + 27 = 10x + 9 - x}$

63 - 9x = 9x + 9

$text{63 - 9x = 9x + 9}$

9x + 9x = 63 - 9

$text{9x + 9x = 63 - 9}$

18x = 54

$text{18x = 54}$

x = \frac{54}{18}

$text{x} = 54/18$

x = 3

$text{x} = 3$

9 - x = 9 - 3 = 6

$text{9 - x} = 9 - 3 = 6$

Put these values in equation (A)

$text{Put these values in equation (A)}$

10(3) + 6 = 36

$text{10(3) + 6 = 36}$

Answer:

$text{Answer:}$

The two digit no. is 36.

$text{The two digit no. is 36.}$

Q4. One of the two digits of a two-digit number is three times the other digit. If you interchange the digits of this two-digit number and add the resulting number to the original number, you get

88

$88$ . What is the original number?

Sol.

$text{Sol.}$

Let tens digit x

$text{Let tens digit x}$

and ones digit 3x

$text{and ones digit 3x}$

original number 10x + 3x

$text{original number 10x + 3x}$ _______

(A)

$text{(A)}$

According to question

$text{According to question}$

(10x + 3x) + [10(3x) + x] = 88

$text{(10x + 3x) + [10(3x) + x] = 88}$

13x + 31x = 88

$text{13x + 31x = 88}$

44x = 88

$text{44x = 88}$

x = \frac{88}{44}

$text{x} = 88/44$

x = 2

$text{x} = 2$

3x = 3 \times 2 = 6

$text{3x} = 3times2 = 6$

Put these values in equation (A)

$text{Put these values in equation (A)}$

10(2) + 6 = 26

$text{10(2) + 6 = 26}$

or

$text{or}$

62

$62$

Answer:

$text{Answer:}$

The original no. is 26 or 62.

$text{The original no. is 26 or 62.}$

Q5. Shobo's mother's present age is six times Shobo's present age. Shobo's age five years from now will be one-third of his mother's present age. What are their present ages?

Sol.

$text{Sol.}$

Let Shobo's present age x years

$text{Let Shobo's present age x years}$

and mother's present age 6x years

$text{and mother's present age 6x years}$

After 5 years

$text{After 5 years}$

Shobo's age x + 5 years

$text{Shobo's age x + 5 years}$

According to question

$text{According to question}$

3(x + 5) = 6x

$text{3(x + 5) = 6x}$

3x + 15 = 6x

$text{3x + 15 = 6x}$

6x - 3x = 15

$text{6x - 3x = 15}$

3x = 15

$text{3x = 15}$

x = \frac{15}{3}

$text{x} = 15/3$

x = 5

$text{x} = 5$

6x = 6 \times 5 = 30

$text{6x} = 6 times 5 = 30$

Answer:

$text{Answer:}$

Shobo's age 5 years and

$text{Shobo's age 5 years and}$

mother's age 30 years.

$text{mother's age 30 years.}$

Q6. There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio

11 : 4

$11 : 4$ . At the rate

$₹ 100$ per meter it will cost the village panchayat

$₹ 75000$ to fence the plot. What are the dimensions of the plot?

$text{Sol.}$

$text{Let Length of rectangular plot 11x}$

$text{and Breadth of rectangular plot 4x}$

$text{According to qiestion}$

$text{Preimeter of rectangular plot = 2(L + B)}$

$text{Total cost of fence}/text{Rate} = text{2(11x + 4x)}$

$75000/100 = text{ 2(15x)}$

$750 = text{ 30x}$

$text{x} = 750/30$

$text{x} = 25$

$text{11x} = 11 times 25 = 275$

$text{4x} = 4 times 25 = 100$

$text{Answer:}$

$text{Length 275 meters and Breadth 100 meters.}$

Q7. Hasan buys two kinds of cloth materials for school uniforms, shirt material that costs him

$₹ 50$ per meter and trouser material that costs him

$₹ 90$ per meter.

For every

$3$ meters of the shirt material, he buys

$2$ meters of the trouser material. He sells the materials at

$12$ % and

$10$ % profit respectively. His total sale is

$₹36600$ . How much trouser material did he buy?

$text{Sol.}$

$text{Ratio of shirt and trouser material bought is 3 : 2}$

$text{Let the shirt material bought 3x}$

$text{and the trouser material bought 2x}$

$text{cost price of shirt material 3x}times 50 = 150text{x}$

$text{cost price of trouser material 2x}times 90 = 180text{x}$

$text{selling price of shirt material =} (text{cp}(100 + p))/100$

$text{sp} = (150text{x}(100 + 12))/100$

$text{sp} = (150text{x} times 112)/100$

$text{sp} = 168text{x}$

$text{selling price of trouser material =} (text{cp}(100 + p))/100$

$text{sp} = (180text{x}(100 + 10))/100$

$text{sp} = (180text{x} times 110)/100$

$text{sp} = 198text{x}$

$text{According to question}$

$text{Total sp = 168x + 198x}$

$text{36600 = 366x}$

$text{x} = 100$

$text{Length of trouser material 2}times 100 = 200text{ m}$

$text{Answer:}$

$text{Length of trouser material 200 m}$

Q8. Half of a herd of deer are grazing in the field and three fourths of the remaining are playing nearby. The rest

$9$ are drinking water from the pond. Find the number of deer in the herd.

$text{Sol.}$

$text{The no. of deer in the herd x}$

$text{and no. of deer are grazing } text{x}/2$

$text{and no. of deer are playing } 3/4times text{x}/2 = (3text{x})/8$

$text{According to question}$

$text{x - x}(1/2 + 3/8) = 9$

$text{x - x}((4 + 3)/8 )= 9$

$text{x - x} (7/8) = 9$

$text{8x - 7x}/8 = 9$

$text{x} = 9times8$

$text{x} = 72$

$text{Answer:}$

$text{The no. of deer in the herd 72.}$

Q9. A grandfather is ten times older than his granddaughter. He is also

$54$ years older than her. Find their present ages.

$text{Sol.}$

$text{Let Granddaughter's present age x years}$

$text{and Grandfather's present age 10x years}$

$text{According to question}$

$text{10x - x = 54}$

$text{9x = 54}$

$text{x} = 54/9$

$text{x} = 6$

$text{10x} = 10 times 6 = 60$

$text{Answer:}$

$text{Granddaughter's present age 6 years and}$

$text{Grandfather's present age 60 years.}$

Q10. Aman's age is three times his son's age. Ten years ago he was five times his son's age. Find their present ages.

$text{Sol.}$

$text{Let son's age x years}$

$text{and Aman's age 3x years}$

$text{Before 10 years}$

$text{son's age (x - 10)}$

$text{and Aman's age (3x - 10)}$

$text{According to question}$

$text{5(x - 10) = (3x - 10)}$

$text{5x - 50 = 3x - 10}$

$text{5x - 3x = 50 - 10}$

$text{2x = 40}$

$text{x} = 40/2$

$text{x} = 20$

$text{3x} = 3times20 = 60$

$text{Answer:}$

$text{Aman's age 60 years and}$

$text{son's age 20 years.}$

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8th Maths 2.4

Chapter 2

Linear Equations in One Variable

NCERT Class 8th solution of Exercise 2.1

NCERT Class 8th solution of Exercise 2.2

NCERT Class 8th solution of Exercise 2.3

NCERT Class 8th solution of Exercise 2.5

NCERT Class 8th solution of Exercise 2.6

Exercise 2.4

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