The ages of Himani and Pushpraj are in the ratio of 8 : 5 respectively. After 9 years the ratio of their ages will be 3 : 2. What is the difference in their present ages? 

Correct option is A

Given:

The ratio of their present ages = 8 : 5

After 9 years, the ratio of their ages will be 3 : 2

Solution:​
Let the present age of Himani be 8x and the present age of Pushpraj be 5x.

After 9 years, their ages will be:

Himani's age = 8x + 9

Pushpraj's age = 5x + 9

According to the given condition, after 9 years, the ratio of their ages will be 3 : 2:

​$$\frac{8x + 9}{5x + 9} = \frac{3}{2}$$​

2(8x + 9) = 3(5x + 9)

16x + 18 = 15x + 27

16x - 15x = 27 - 18

x = 9

Now, the present ages are:

Himani's age = 8x = 8 × 9 = 72 years

Pushpraj's age = 5x = 5 × 9 = 45 years

The difference in their present ages is:

72 − 45 = 27 years

Thus, the difference in their present ages is 27 years.