Question

Two numbers are in the ratio 5 : 9. On subtracting 3 from each, the ratio becomes 1 : 2. Find the numbers.

Answer 1

Suppose that the numbers are 5x and 9x.
Then, (5x − 3) : (9x − 3) = 1 : 2

⇒ $\frac{5x-3}{9x-3}=\frac{1}{2}$

⇒ 10x − 6 = 9x − 3
⇒ x = 3

Hence, the numbers are (5 $\times$ 3 =) 15 and (9 $\times$ 3 =) 27.