If the ratio of the ages (in years) of P and Q, 5 years ago was 5 : 7 , then the sum of their ages 5 years from now is _____ years.

Given:

The ratio of ages of P and Q, 5 years ago = 5 : 7

Formula used:

If the ratio of ages is a : b, then their ages can be represented as:

P's age = 5x, Q's age = 7x (where x is the multiplier)

Sum of their ages after 5 years = (P's age + 5) + (Q's age + 5)

Calculation:

5 years ago, P's age = 5x and Q's age = 7x

⇒ Current ages:

P's age now = 5x + 5

Q's age now = 7x + 5

⇒ After 5 years:

P's age = (5x + 5) + 5 = 5x + 10

Q's age = (7x + 5) + 5 = 7x + 10

⇒ Sum of their ages after 5 years:

(5x + 10) + (7x + 10) = 12x + 20

Now, we will solve this equation using the Options.

Here we will put the value of x as 1, 2 ,3 and so on.

When we put the value of x = 6

We get, (12 × 6) + 20 = 72 + 20 = 92.

∴ The correct answer is Option 4).