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Present age of father is 42 years and that of his son is 14 years. Find the ratio of
(a) Present age of father to the present age of son.
(b) Age of the father to the age of son, when son was 12 years old.
(c) Age of father after 10 years to the age of son after 10 years.
(d) Age of father to the age of son when father was 30 years old.

Solution:

The present age of father = 42 years

The present age of son = 14 years

(a) Ratio of the present age of father to the present age of son = Present age of father / Present age of the son

= 42 / 14

= 3 : 1

Therefore, 3:1 is the ratio of the present age of the father to the present age of the son.

(b) The son's age will be 12 two years back (14 - 2 = 12) , so we will calculate the father's age two years ago.

Hence, two years ago father's age will be = 42 – 2 = 40 years

Hence, required ratio = 40 / 12

= (4 × 10) / (4 × 3)

= 10 / 3

Therefore, 10:3 is the ratio of the father's age to the son's age, when the son was 12 years old.

(c) Father will be 52 years old after 10 years ( 42 + 10 = 52 years)

Son's age after 10 years = 14 + 10 = 24 years

Hence, required ratio = 52 / 24

= (4 × 13) / (4 × 6)

= 13 / 6

Therefore, the ratio of the father's age after 10 years to the son's age after 10 years is 13 : 6.

(d) 12 years ago father’s age was 30 years (42 - 12 = 30)

Age of son at that time = 14 – 12 = 2 years

Required ratio = 30 / 2

= (2 × 15) / 2

= 15 / 1

Therefore, the ratio of father's age to the son's age when father was 30 years old is 15:1

NCERT Solutions for Class 6 Maths Chapter 12 Exercise 12.1 Question 16

Present age of father is 42 years and that of his son is 14 years. Find the ratio of (a) Present age of father to the present age of son. (b) Age of the father to the age of son, when son was 12 years old. (c) Age of father after 10 years to the age of son after 10 years. (d) Age of father to the age of son when father was 30 years old.

Summary:

It is given that the present age of the father is 42 years and that of his son is 14 years. The ratio of (a) the Present age of the father to the present age of the son is 3:1. (b) Age of the father to the age of the son, when the son was 12 years old is 10:3.c(c) Age of father after 10 years to the age of son after 10 years is 13:6 (d) Age of father to the age of son when father was 30 years old is 15:1

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