Question

A mother is now 2 and ahalf times old as her daughter Mary. Four years ago the ratio of their ages was 3:1. Find the present age of the mother.

Answer 1

Given:

A mother is now 2 and a half times old as her daughter Mary.

Four years ago the ratio of their ages was 3:1.

To find:

The present age of the mother.

Solution:

Let x be the present age Mary's mother and y be the present age of Mary.

A mother is now 2 and a half times old as her daughter Mary. So,

$x=2\dfrac{1}{2}y$

$\dfrac{x}{y}=\dfrac{2(2)+1}{2}$

$\dfrac{x}{y}=\dfrac{5}{2}$

It means the ratio of their present age is 5:2. Let 5z be the present age of Mary's mother and 2z be the present age of Mary.

Four years ago the ratio of their ages was 3:1.

$\dfrac{5z-4}{2z-4}=\dfrac{3}{1}$

$1(5z-4)=3(2z-4)$

$5z-4=6z-12$

$-4+12=6z-5z$

$8=z$

Now, the present age of the mother is:

$5z=5(8)$

$5z=40$

Therefore, the present age of the mother is 40 years.