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. What is the average of a, b, c, d, e and f?
It is given,
$$\ \frac{\ a+b+c}{3}=11$$
a + b + c = 33 ...... (1)
$$\ \frac{\ c+d+e}{3}=17$$
c + d + e = 51 ...... (2)
$$\ \frac{\ e+f}{2}=22$$
e + f = 44 ...... (3)
$$\ \frac{\ e+c}{2}=17$$
e + c = 34 ...... (4)
(1) + (2) + (3) - (4) we get the sum of a, b, c, d, e and f
a + b + c + d + e + f = (a+b+c) + (c+d+e) + (e+f) - (e+c) = 33 + 51 + 44 - 34 = 94
Average = $$\frac{94}{6}=\frac{47}{3}=15\frac{2}{3}$$
The answer is option A.
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