NCERT Solution (Ex - 2.4) - Chapter 2: Linear Equations in one variable, Maths, Class 8 PDF Download

Linear Equations in one variable

Exercise 2.4

Question 1:
Amina thinks of a number and subtracts 5 / 2 from it. She multiplies the result by 8. The result now obtained is 3 times the same number she thought of. What is the number?

Answer 1:
Let Amina think a number x.
According to the question, 

Hence, the number is 4.

Question 2:
A positive number is 5 times another number. If 21 is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers?

Answer 2:
Let another number be x.
Then positive number = 5x
According to the question,   5x+21 = 2(x+21)

 5x+21 = 2x+42

 5x-2x=  42-21

 3x=21

 x =21/3 =7

Hence another number = 7 and positive number = 5 x 7 =35

Question 3:
Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the twodigit number?

Answer 3:
Let the unit place digit of a two-digit number be x.
Therefore, the tens place digit = 9 - x
 2-digit number = 10 x tens place digit + unit place digit
Original number = 10(9 - x) + x
According to the question, New number = Original number + 27

Hence, the 2-digit number = 10(9-x)+x=10(9-6)+6= 10*3+6- 30+6 =36

Question 4:
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. What is the original number?

Answer 4:
Let the unit place digit of a two-digit number be x.
Therefore, the tens place digit = 3x
2-digit number = 10 x tens place digit + unit place digit

Original number = 10*3x+x=30x+x=31x

According to the question, New number + Original number = 88

Hence, the 2-digit number = 31x = 31*2 = 62

Question 5:
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 age?

Answer 5:
Let Shobo’s present age be x years.
And Shobo’s mother’s present age = 6x years
According to the question,  

 x+5=2x

2x= x+5

2x-x=5

 x=5 years

Hence, Shobo’s present age = 5 years and Shobo’s mother’s present age = 6 x 5 = 30 years

Question 6:
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. At the rate ` 100 per meter it will cost the village panchayat ` 75,000 to fence the plot. What are the dimensions of the plot?

Answer 6:
Let the length and breadth of the rectangular plot be 11x and 4x respectively.

We know that Perimeter of rectangle = 2 (length + breadth)
Therefore, according to the question, 750=2(11x+4x)

Hence, length of rectangular plot = 11 x 25 = 275 m and breadth of rectangular plot = 4 x 25 = 100 m

Question 7:
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 2 meters of the trouser material he buys 3 meters of the shirt material. He sells the materials at 12% and 10% respectively. His total sale is ₹36,000. How much trouser material did he buy?

Answer 7:
Let ratio between shirt material and trouser material be 3x : 2x.

The cost of shirt material = 50*3x = 150x

The selling price at 12% gain 

The cost of trouser material = 90*2x =180x

The selling price at 12% gain

According to the question, 168x +198x = 36,600

Now, trouser material = 2x = 2 x 100 = 200 meters
Hence, Hasan bought 200 meters of the trouser material.

Question 8:
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.
Answer 8:
Let the total number of deer in the herd be x.
According to question,  

Hence, the total number of deer in the herd is 72.

Question 9:
A grandfather is ten times older than his granddaughter. He is also 54 years older than her. Find their present ages.

Answer 9:
Let present age of granddaughter be x years.
Therefore, Grandfather’s age = 10x years
According to question   10x=x+54

Hence, granddaughter’s age = 6 years and grandfather’s age = 10 x 6 = 60 years.

Question 10:
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.

Answer 10:
Let the present age of Amon’s son be x years.
Therefore, Aman’s age = 3x years
According to question,       3x-10 =5(x-10)

 3x-10= 5x-50

 3x-5x=-50+10

  -2x= -40

 x=-40/-2= 20

Hence, Aman’s son’s age = 20 years and Aman’s age = 3 x 2 = 60 years