The ages of Himani and Pushpraj are in the ratio of 9 : 7 respectively. After 6 years the ratio of their ages will be 5 : 4. What is the difference in their present ages?

Correct option is C

Given:

The current ratio of the ages of Himani and Pushpraj is 9 : 7.

After 6 years, the ratio of their ages will be 5 : 4.

Solution:

Let the present ages of Himani and Pushpraj be 9x and 7x respectively, where x is a common factor.

Write the ages after 6 years:

Himani's age after 6 years = 9x + 6

Pushpraj's age after 6 years = 7x + 6

According to the problem, after 6 years, the ratio of their ages will be 5 : 4. Therefore, we have:

$$\frac{9x + 6}{7x + 6} = \frac{5}{4}$$​

Expanding both sides:

36x + 24 = 35x + 30

36x − 35x = 30 − 24

x = 30 - 24

x = 6

Himani's present age = 9x = 9 × 6 = 54

Pushpraj's present age = 7x = 7 × 6 = 42

Difference = 54 - 42 = 12 years
The difference in their present ages is 12 years.