# Class 8 Maths NCERT Solutions for Chapter – 2 Linear Equations In One Variable Ex – 2.4

### Linear Equations In One Variable

Question 1.
Amina thinks of a number and subtracts $\frac { 5 }{ 2 }$ 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 ?

Solution.
Let Amina thinks of a number x. It is given that

Hence, the number thought 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 ?

Solution.
Let the numbers be x and 5x. it is given that

Hence, the required numbers are 7 and 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 two-digit number ?

Solution.
Let the unit’s digit be x.

∴ Unit’s digit = 6 and ten’s digit = 3
Hence, the number = 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 ?

Solution.
Let one’s digit be x. Then, ten’s digit 3x.

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 ages ?

Solution.
Let the present age of Shobo be x years. Then,

∴ Present age of Shobo = 5 years ,
∴ Present age of his mother = 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 of ₹ 100 per metre it will cost the village panchayat ₹ 75000 to fence the plot. What are the dimensions of the plot ?

Solution.
Let the length and breadth of the rectangular plot be 11x and 4x metres. Then,

Question 7.
Hasan buys two kinds of cloth materials for school uniforms, shirt material that costs him ₹ 50 per metre and trouser material that costs him ₹ 90 per metre. For every 2 meters of the trouser material he buys 3 metres of the shirt material. He sells the materials at 12% and 10% profit respectively. His total sale is ₹ 36,600. How much trouser material did he buy ?

Solution.
Let material bought for trousers and shirts be 2x metres and 3x metres respectively.
Cost price of 2x metres of trouser material @ ₹ 90 per metre = ₹ (90 x 2x) = ₹ 180x
Cost price of 3x metres of shirt material @ ₹ 50 per metre = ₹ (50 x 3x) = ₹ 150x

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.

Solution.
Let the number of deer in the herd be x. Then,

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

Solution.
Let the present age of grand daughter be x years. Then, the present age of grandfather is 10x years
According to the question.
10x – x = 54 ⇒ 9x = 54
⇒  $x=\frac { 54 }{ 9 } =6$
∴ Granddaughter’s age = 6 years
and grandfather’s age = 10 x 6 = 60 years.

Question 10.
Am.an’s age is three times his son’s age. Ten years ago he was five times his son’s age. Find their present ages.

Solution.
Let the present age of son be x years. Then, the age of his father Aman is 3x.
10 years ago : Their ages will be (x – 10) years and (3x – 10) years respectively.