Three taps A, B and C together can fill an empty cistern in 10 min. The tap A alone can fill it in 30 min and the tap B alone can fill it in 40 min. How long will the tap C alone take to fill it?

A) 16 min

B) 24 min

C) 32 min

D) 40 min

Correct answer:
B) 24 min

Description for Correct answer:
Part filled by (A+B+C) in 1 min = \( \Large \frac{1}{10} \)

Part filled by A in 1 min = \( \Large \frac{1}{30} \)

Part filled by B in 1 min = \( \Large \frac{1}{40} \)

Part filled by (A + B) in 1 min = \( \Large \frac{1}{30} \) + \( \Large \frac{1}{40} \)

= \( \Large \frac{4+3}{120} \) = \( \Large \frac{7}{120} \)

Therefore, Part filled by C in 1 min

= \( \Large \frac{1}{10} \) - \( \Large \frac{7}{120} \)=\( \Large \frac{12-7}{120} \)=\( \Large \frac{5}{120} \)=\( \Large \frac{1}{24} \)

Therefore, Tap C will fill the cistern in 24 min.


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