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.