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A tank is connected to 4 taps among which two are inlet taps and two are outlet taps. Inlet taps can fill the tank in 10 and 15 minutes when tank is empty, while outlet pipes can empty the full tank in 12 and 20 minutes. In how many minutes an empty tank can be filled when all the taps are opened simultaneously?

A tank is connected to 4 taps among which two are inlet taps and two are outlet taps. Inlet taps can fill the tank in 10 and 15 minutes when tank is empty, while outlet pipes can empty the full tank in 12 and 20 minutes. In how many minutes an empty tank can be filled when all the taps are opened simultaneously? Correct Answer 30 minutes

Let the inlet taps be A and B, and outlet taps be C and D.

As, Tap A can fill the tank in 10 minutes

⇒ Part of tank filled by A in 1 minute = 1/10

Also, Tap B can fill the tank in 15 minutes

⇒ Part of tank filled by tap B in 1 minute = 1/15

⇒ Part of tank filled by Tap A and B in 1 minute = (1/10) + (1/15) = 1/6

Now, Tap C can empty the tank in 12 minutes

⇒ Part of tank emptied by tap C in 1 minute = 1/12

Also, Tap D can empty the tank in 20 minutes

⇒ Part of tank emptied by tap D in 1 minute = 1/20

⇒ Part of tank emptied by tap C and D in 1 minute = (1/12) + (1/20) = 2/15

⇒ Effective filling of tank in 1 minute when all the taps are open = (1/6) – (2/15) = 1/30

∴ The tank will be filled in 30 minutes

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