The ages of A and B are in the ratio of 11 : 13 respectively. After 7 years the ratio of their ages will be 20 : 23. What is the difference in years between their ages?

Let the present ages of A and B are 11x and 13x years respectively; then
According to question,
After 7 years the ratio of their ages will be 20 : 23.
(11x + 7 ) / (13x + 7) = 20/23
⇒ (11x + 7 ) 23 = 20 (13x + 7)
⇒ 253x + 161 = 260x + 140
⇒ 7x = 21
∴ x = 3
Hence, difference of their ages = 13x - 11x = 2x = 2 x 3 = 6 years