Multiple choice

Passage

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?

  1. 12

  2. 13

  3. 14

  4. 15
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Solving the system of equations based on the passage: D=3A, C=B-(G-E), G-E=E-D, (D+G)/2=16, (A+E)/2=11, (B+C)/2=11. From these, D+G=32, A+E=22, B+C=22. The average of B, C, D, E, G is (B+C+D+E+G)/5. Since B+C=22 and D+G=32, we need E. Using D=3A and D+G=32, and E-D=G-E => 2E=D+G=32, so E=16. Then A = (22-16)=6. D = 3*6=18. G = 32-18=14. Sum = 22 + 32 + 16 = 70. Average = 70/5 = 14.

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