###
**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**

## Show Answer

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

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