Question

Ratio of the present age of Nath and his mother is 3:7. At the time of Nath birth his mother age was 20 years . Find the present ages of Nath and his mother ​

Answer 1

Given :-

Ratio of the present age of Nath and his mother is 3:7.

At the time of Nath birth his mother age was 20 years.

To Find :-

The present age of Nath.

The present age of Nath's mother.

Analysis :-

Consider Nath's age as a variable and mother's age will be the variable added to the age she was at the birth of Nath.

Make an equation accordingly.

Get the value of the variable and substitute it in the mother's age.

Solution :-

Let Nath's present age be 'x' and mother's age would be 'x + 20'.

Making an equation,

$\sf \dfrac{x}{x+20} =\dfrac{3}{7}$

$\sf 7x = 3 (x + 20)$

$\sf 7x=3x+60$

$\sf 7x-3x=60$

$\sf 4x=60$

Finding the value of x,

$\sf x=\dfrac{60}{4}$

$\sf x=15$

Nath's present age = 15 years

Mother's age = x + 20

= 15 + 20 = 35 years

Therefore, Nath's and his mother's age is 15 and 35 years respectively.

Answer 2

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