### 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 Apex 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 $\begin{array}{l} =\large\frac{94}{6} \\ =\large\frac{47}{3} \\ =15 \frac{2}{3} \end{array}$

A. 20
B. 21
C. 28
D. 32

A. 18
B. 20
C. 24
D. 30

A. 10 years
B. 10.5 years
C. 11 years
D. 12 years