Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is:

A. 10

B. 12

C. 14

D. 16

Answer: Option C

Solution(By Examveda Team)

Part filled in 2 hours = $$\frac{2}{6}$$ = $$\frac{1}{3}$$
Remaining part = $$ {1 - \frac{1}{3}} $$  = $$\frac{2}{3}$$
∴ (A + B)'s 7 hour's work = $$\frac{2}{3}$$
(A + B)'s 1 hour's work = $$\frac{2}{{21}}$$
∴ C's 1 hour's work = {(A + B + C)'s 1 hour's work} - {(A + B's 1 hour's work}
$$\eqalign{ & = {\frac{1}{6} - \frac{2}{{21}}} \cr & = \frac{1}{{14}} \cr} $$
∴ C alone can fill the tank in 14 hours