Question

The age of three members of a family P, Q, and R are in the ratio of 12 : 15 : 25. Sum of their ages is 416. Find the ratio between the difference of age of Q and P and the difference of R and Q.

• A. 3 : 10
• B. 10 : 3
• C. 4 : 5
• D. 5 : 4

Answer 1

Answer:

A. 3 : 10

Let the age of P, Q, and R = 12a, 15a, 25a
The Sum of their ages = 416
⇒ 12a + 15a + 25a = 416
⇒ 52a = 416
⇒ a = 8 years
Age of P = 96 years
Age of Q = 120 years
Age of R = 200 years
⇒ Difference of age of Q and P : difference of R and Q
⇒ 120 – 96 : 200 – 120
⇒ 24 : 80
⇒ 3 : 10
Alternate method

The ages of P, Q and R = 12x, 15x and 25x
Difference between their ages:
Q - P = 3x
R - Q = 10x
Ratio between difference of ages = 3x ∶ 10x = 3 ∶ 10