The ages of A and B are in the ratio of 5: 3. After 5 years the ratio of their ages will be 10: 7. What is the difference between present ages of A and B (in years)

Correct option is D

​Given:

Present age ratio of $$A : B = 5 : 3.$$​

After 5 years, age ratio = 10 : 7.

Solution:

Let present ages of A and B be 5x and 3x, respectively.

After 5 years:

​$$\frac{5x + 5}{3x + 5} = \frac{10}{7}$$​​

​$$7(5x + 5) = 10(3x + 5)\\ \ \\ \implies 35x + 35 = 30x + 50$$​​

​$$5x = 15 \implies x = 3$$​​

Present ages:

​$$A = 5x = 15, \, B = 3x = 9$$​​

Difference of ages 

​$$A - B = 15 - 9 = 6$$ years