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?

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Solution

The correct option is C
14

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

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

$∴$ C alone can fill the tank in 14 hours.

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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?

The correct option is C 14 Part filled in 2 hours =26=13 Remaining part = (1−13)=23 ∴ (A + B)'s 7 hour's work = 23 (A + B)'s 1 hour's work = 221 C's 1 hour's work = [(A + B + C)'s 1 hour's work – (A + B)'s 1 hour's work] =(16−221)=114 ∴ C alone can fill the tank in 14 hours.

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?