Question

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.
How many hours will be taken by C alone to fill the tank?

• A. 10
• B. 12
• C. 14
• D. 16
• E. 18

Answer 1

The correct option is C

14

Part filled in 2 hours $=\frac{2}{6}=\frac{1}{3}$
Remaining part = $(1-\frac{1}{3})=\frac{2}{3}$

$\therefore$ (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] $=(\frac{1}{6}-\frac{2}{21})=\frac{1}{14}$

$\therefore$ C alone can fill the tank in 14 hours.