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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 farher to the age of son when father was 30 years old.

Given:

The present age of the father is 42 years and that of his son is 14 years.

To do:

We have to find the ratio of the given statements.

Solution:

(a) The present age of the father $=42\ years$

The present age of the son $=14\ years$

The ratio of the present age of the father to the present age of the son $=\frac{42}{14}$

$=\frac{3}{1}$

The ratio of the present age of the father to the present age of the son is $3 : 1$.

(b) The age of the father when the son was 12 years old $=42-2$

$=40\ years$

The ratio of the age of the father to the age of the son when the son was 12 years old $=\frac{40}{12}$

$=\frac{10}{3}$

The age of the father to the age of the son, when the son was 12 years old is $10 : 3$.

(c) The present age of the father $=42\ years$

The age of the father after 10 years $=42\ years+10\ years$

$=52\ years$

The present age of the son $=14\ years$

The age of the son after 10 years $=14\ years+10\ years$

$=24\ years$

The ratio of the age of the father after 10 years to the age of the son after 10 years$=\frac{52}{24}$

$=\frac{13}{6}$

The ratio of the age of the father after 10 years to the age of the son after 10 years is $13 : 6$.

(d) The present age of the father $=42\ years$

We have,

The age of the father $=30\ years$

This implies,

The difference between the present age of the father and the age of the father when he was 30 years old $=42-30$

$=12\ years$

The age of the son when the father was 30 years $=14-12$

$=2\ years$

The ratio of the age of the father to the age of the son when the father was 30 years old$=\frac{30}{2}$

$=\frac{15}{1}$

The ratio of the age of the father to the age of the son when the father was 30 years old is $15 : 1$.

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