Pipes A and B can fill a tank in 10 hours and 15 hours respectively and pipe C can empty it in 30 hours. If all the pipes are opened together in the empty tank then in how much time will it be full ?

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$\frac{15}{2} hours$

$\frac{14}{3} hours$

$\frac{15}{4} hours$

$\frac{7}{3} hours$

answer is A.

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Detailed Solution

$A c a n f i l l a tank = 10 h r s \Rightarrow f o r 1 h r = \frac{1}{10}$

$B c a n f i l l a tank = 15 h r s \Rightarrow f o r 1 h r = \frac{1}{15}$

$C c a n e m p t y t h e tank = 30 h r s \Rightarrow f o r 1 h r = \frac{1}{30}$

$∴ A + B + C = \frac{1}{10} + \frac{1}{15} - \frac{1}{30} = \frac{3 + 2 - 1}{30}$

$A + B - C = \frac{5 - 1}{30} = \frac{4}{30} \Rightarrow \frac{30}{4} = \frac{15}{2} h o u r s$

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