The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages, in years, of the son and the father are, respectively
a. 4 and 24
b. 5 and 30
c. 6 and 36
d. 3 and 24

Solution:

Given, the father's age is six times his son’s age.

We have to find the present ages of the father and the son.

Let the present age of the father be x years.

Let the present age of the son be y years.

Given, x = 6y ------------- (1)

After 4 years, the father's age is four times his son’s age.

(x + 4) = 4(y + 4)

x + 4 = 4y + 16

x - 4y = 16 - 4

x - 4y = 12 ----------- (2)

For solving the linear equations (1) and (2), substitute (1) in (2),

6y - 4y = 12

2y = 12

y = 12/2

y = 6

Put y = 6 in (1),

x = 6(6)

x = 36

Therefore, the present ages of the father and the son are 36 years and 6 years.

✦ Try This: If the sum of the ages of a father and his son in years is 65 and twice the difference of their ages in years is 50, then the age of the father is: a. 40, b. 45, c. 50, d. 55

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3

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NCERT Exemplar Class 10 Maths Exercise 3.1 Problem 13

The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages, in years, of the son and the father are, respectively, a. 4 and 24, b. 5 and 30, c. 6 and 36, d. 3 and 24

Summary:

The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages, in years, of the son and the father are, 6 years and 36 years respectively

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