The ratio of the present age of the two brothers is 11: 13 and 6 years ago the ratio of their ages was 4: 5. What will be the ratio of their ages after 5 years?

Correct option is C

Given:
Present age ratio = 11:13
6 years ago age ratio = 4:5
Solution:
Let the present ages of the two brothers be 11x and 13x
Six years ago, their ages were 11x - 6 and 13x - 6 respectively.
According to the problem, six years ago, the age ratio was 4:5:
​$$\frac{11x - 6}{13x - 6} = \frac{4}{5}$$​​
5(11x - 6) = 4(13x - 6)
55x - 30 = 52x - 24
3x = 6
x = 2
Therefore, the present ages are $$11 \times 2 = 22\, \text{and}\, 13 \times 2 = 26$$​​
After 5 years, their ages will be:
22 + 5 = 27 and 26 + 5 = 31
The ratio of their ages after 5 years will be 27:31.