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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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