# 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.

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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 $15 : 1$.

Updated on 10-Oct-2022 13:36:48