The age of the two friends were in the ration of 6:5. If the sum of their ages is 55. Then after how many years their ratio will become 8:7?

a. 11

b. 7

c. 10

d. 12

Ratio is 6:5, the sum is 55.

6x + 5x = 55

11x = 55

x = 55/11

x = 5

Their ages now are:

6*5 = 30 years old

5*5 = 25 years old

Lets find their ages for the ratio of 8:7

Let y = years:

30 + y / 25 + y = 8/7

Cross multiply:

8 (25 + y) = 7 (30 + y)

200 + 8y = 210 + 7y

y = 10

The answer is C. 10