A, B, C, D, E, F and G are cousins. D is thrice as old as A. Further, C is as many years younger to B, as G to E and E to D. The average age of D and G is 16 years; the average age of A and E is 11 years; the average age of B and C is also 11 years. B and C have equal weight. A's weight is 10 kg less than that of B; D is 4 kg heavier than E; E is 4 kg heavier than F; F is 4 kg heavier than G. Further, D has age-weight ratio of 9 : 20, where age is in years and weight in kg; A has age-weight ratio of 2 : 5. Moreover, none of them is more than 40 kg. What is the average age (in years) of B, C, D, E and G?
- A12
- B13
- C14
- D15
Explanation
From the averages: D + G = 32, A + E = 22, B + C = 22. The equal age-gap condition makes D, E, G an arithmetic progression, so E is the middle term: E = 16. Then A = 22 − 16 = 6, D = 3A = 18 (D is thrice A's age), and G = 32 − 18 = 14. The ages B, C, D, E, G sum to 22 + 18 + 16 + 14 = 70, so their average is 70/5 = 14 years, option (C).