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### 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 **

Here is complete explanation of Average of a b and c is 11 average of c….

__Solution(By ExamCraze 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

= $$frac{94}{6}$$

= $$frac{47}{3}$$

= $$15frac{2}{3}$$