Question

The ratio of ages of a and b are in the ratio 5: 6. If the sum of their ages is 55, in how many years will the ratio of their ages be 6:7?

Answer 1

Let the ratio to be 5x and 6x
$5x + 6x = 55 \\ x = \frac{55}{11 } \\ x = 5$
Their ages are 25 and 30 years
Now let their ages would be in the ratio 6:7 after y years
As per condition
$\frac{25 + y}{30 + y} = \frac{6}{7} \\ 175 + 7y = 180 + 6y \\ y = 5$