Previous Year Questions

Here, (P - 7) + (Q - 7) + (R - 7) = 31

P + Q + R = 52

Q is the eldest and P is 4 years younger to R. Then,

Q > R > P

P = R - 4

The difference between the ages of Q and R is more than 3 but less than 7. Then,

7 > Q - R > 3

Case 1: when Q = R + 4

Then, R - 4 + R + 4 + R = 52

3R = 52

R = 52/3 (but present ages of P, Q and R are integers)

So, this case is invalid.

Case 2: when Q = R + 5

R - 4 + R + 5 + R = 52

3R = 51

R = 17

Case 3: when Q = R + 6

R - 4 + R + 6 + R = 52

3R = 50

R = 50/3 (but present ages of P, Q and R are integers)

So, this case is invalid.

So, only one possible age of R, i.e., 17 years.