Pipes A and B can fill a tank in 5 and 6 h, respectively. Pipe C can fill it in 30 h. If all the three pipes are opened together, then in how much time the tank will be filled up?

A) \( \Large 3\frac{3}{14} \) h

B) \( \Large 2\frac{1}{2} \) h

C) \( \Large 3\frac{9}{14} \) h

D) \( \Large 2\frac{1}{14} \) h

Correct answer:
B) \( \Large 2\frac{1}{2} \) h

Description for Correct answer:

Part filled by A in 1 h = \( \Large \frac{1}{5} \)

Part filled by B in 1 h = \( \Large \frac{1}{6} \)

Part filled by C in 1 h = \( \Large \frac{1}{30} \)

Net part filled by (A + B + C) in 1 h

= \( \Large \left(\frac{1}{5}+\frac{1}{6}+\frac{1}{30}\right) \)

= \( \Large \frac{6+5+1}{30} = \frac{12}{30} \) = \( \Large \frac{2}{5} \)

Therefore, Required time to fill the tank = \( \Large \frac{5}{2} \)h = \( \Large 2\frac{1}{2} \) h



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