Question

The ages of a and b are in the ratio 5:7 eight year ago , their ages were in the ratio 2:5 find their present ages​

Answer 1

Given :-

Ratio of the ages A and B = 5 : 7

Ratio of their ages 8 years ago = 2 : 5

To Find :-

The present age of A.

The present age of B.

Analysis :-

Consider the present ages as two different variables.

Make an equation according to the two cases.

Then substitute the values and solve it accordingly.

Solution :-

Let the present ages of A and B be '5x' and '7x' respectively.

8 years ago,

$\sf \dfrac{5x-8}{7x-8} =\dfrac{2}{5}$

According to the question,

$\sf 5(5x-8)=2(7x-8)$

$\sf 25x-40=14x-16$

Picking the like terms,

$\sf 25x-14x=40-16$

$\sf 11x=24$

Finding the value of x,

$\sf x=\dfrac{24}{11}$

$\sf x=2.182$

Finding the present ages,

Present age of A = 5x

= 5 × 2.182 = 10.91 years

Present age of B = 7x

= 7 × 2.182 = 10.274 years

Therefore, the ages of A and B are 10.91 years and  years respectively.