Question

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

Answer 1

Let the two numbers be 'x' and 'y'.
Given that x : y = 7 : 11 = $\frac{x}{y}=\frac{7}{11}$ = x = $\frac{7y}{11}$ ------- (1)
Now, 7 is added to each of the numbers, which means that
$\frac{x+7}{y+7}=\frac{2}{3}$
$\frac{{\displaystyle \frac{7y}{11}}+7}{y+7}$ = $\frac{2}{3}$
$\frac{{\displaystyle \frac{7y+77}{11}}}{y+7}$ = $\frac{2}{3}$
3 (7y + 77) = 2 $\times$ 11 (y + 7)
21y + 231 = 22y + 154
22y $-$ 21y = 231 $-$ 154
Therefore, y = 77, and x = $\frac{7y}{11}$ = $\frac{7\times 77}{11}$= 49.
Thus, the two numbers are 49 and 77.