Question

Two numbers are in the ratio 7 : 11. If added to each of the numbers, the ratio becomes 2 : 3. Find the numbers.

Answer 1

Suppose that the numbers are 7x and 11x.

Then, (7x + 7) : (11x + 7) = 2 : 3
⇒ $\frac{7x+7}{11x+7}=\frac{2}{3}$

⇒ 21x + 21 = 22x + 14

⇒ x = 7

Hence, the numbers are (7 $\times$ 7 =) 49 and (11 $\times$ 7 =) 77.