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

Three taps A, B and C together can fill an empty cistern in 10 minutes. The tap A alone can fill it in 30 minutes and the tap B alone in 40 minutes. How long will the tap C alone take to fill it?
[A]40 minutes
[B]32 minutes
[C]16 minutes
[D]24 minutes

24 minutes
Part of the cistern filled by taps A, B and C in 1 minutes = $latex \frac{1}{10}&s=1$
Part of the cistern filled by taps A and B in 1 minutes = $latex \frac{1}{30}+\frac{1}{40}=\frac{4+3}{120}=\frac{7}{120}&s=1$
∴ Part of the cistern filled by tap C in 1 minute =
$latex = \frac{1}{10}-\frac{7}{120} = \frac{12-7}{120} = \frac{5}{120} = \frac{1}{24}&s=1$
∴ Tap C will fill the cistern in 24 minutes.
Hence option [D] is the right answer.


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