Question

The ages of A and B are in the ratio 5 : 7. Four years from now the ratio of their ages will be 3 : 4. The present age of B is

(a) 20 years

(b) 28 years

(c) 15 years

(d) 21 years

Answer 1

Ages of A : B = 5 : 7

Let A's age = 5x

Then B's age = 7x

After 4 years

A's age = 5x + 4

and B's age = 7x + 4

$\therefore \frac{5x+4}{7x+4}=\frac{3}{4}\Rightarrow 3(7x+4)=4(5x+4)21x+12=20x+16\Rightarrow 21x-20x=16-12\Rightarrow x=4$

$\therefore$ B's age = 7x = 7 $\times$ 4 = 28 years