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 D's age (in years)?
- A15
- B16
- C17
- D18
Explanation
The age conditions give D = 3A, D + G = 32, A + E = 22, and B − C = E − G = D − E (equal gaps). From A + E = 22, E = 22 − A; then D − E = 3A − (22 − A) = 4A − 22, and G = E − (D − E) = 44 − 5A. Using D + G = 32: 3A + 44 − 5A = 32, so A = 6 and D = 18. The weight ratios confirm consistency: D's age:weight = 9:20 gives weight 40 kg, A's 2:5 gives 15 kg, fitting all the stated differences with nobody over 40 kg. The answer is (D) 18.