Average of a, b, and c is 11; average of c, d and e is 17; average of e and f is 22 and average of e and c is 17. Find out the average of a, b, c, d, e and f.

A. $$15\frac{2}{3}$$

B. $$18\frac{1}{2}$$

C. $$16\frac{1}{2}$$

D. None of these

Answer: Option A

Solution(By Examveda Team)

Average of a, b and c = 11
Total of a, b and c = 33.....(i)
Similarly, average of c, d and e = 17
Sum of c + d + e = 3 × 17 = 51.....(ii)
Average of e and f is 22
Sum of e + f = 2 × 22 = 44.....(iii)
Average of e and c is 17
Sum of e + c = 2 × 17 = 34.....(iv)
By equations (i) + (ii) + (iii) - (iv)
a + b + c + c + d + e + e + f - e - c
= 33 + 51 + 44 - 34
= 128 - 34
= 94
∴ Required average
= $$\frac{94}{6}$$
= $$\frac{47}{3}$$
= $$15\frac{2}{3}$$