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5 taps are connected to a tank among which 3 taps (A, B and C) are inlet taps and 2 taps (P and Q) are outlet taps. A, B and C can fill the tank in 24 minutes, 30 minutes and 36 minutes respectively while taps P and Q can empty the tanks in 15 minutes and 45 minutes respectively. If tap B is opened after 5 minutes and tap P is opened 5 minutes after tap B, find the time taken to fill the tank completely.

5 taps are connected to a tank among which 3 taps (A, B and C) are inlet taps and 2 taps (P and Q) are outlet taps. A, B and C can fill the tank in 24 minutes, 30 minutes and 36 minutes respectively while taps P and Q can empty the tanks in 15 minutes and 45 minutes respectively. If tap B is opened after 5 minutes and tap P is opened 5 minutes after tap B, find the time taken to fill the tank completely. Correct Answer 36 minutes

Tap A can fill the tank in 24 minutes

⇒ In 1 minute tank filled with A = 1/24

Tap B can fill the tank in 30 minutes

⇒ In 1 minute tank filled with B = 1/30

Tap C can fill the tank in 36 minutes

⇒ In 1 minute tank filled with C = 1/36

Tap P can empty the tank in 15 minutes

⇒ In 1 minute, it can empty 1/15 part of tank.

Tap Q can empty the tank in 45 minutes

⇒ In 1 minute, it can empty 1/45 part of tank.

Initially tap A, C and Q are opened for 5 minutes

⇒ Tank filled in first 5 minutes = 5 × (1/24 + 1/36 – 1/45)

⇒ 5 × (5/72 – 1/45) = 85/360

Tap B is also opened for next 5 minutes.

So, the tank filled in next 5 minutes = 85/360 + 5 × 1/30

⇒ 145/360

Tank filled in first 10 minutes = 85/360 + 145/360 = 23/36

Now, tap P is also opened

Effective filling of tank in 1 minute = (1/24 + 1/30 + 1/36) – (1/15 + 1/45)

⇒ 37/360 – 32/360

⇒ 5/360 = 1/72

We need to fill 13/36 part of tank now

It will take 26 minutes more to fill the tank completely.

Total time taken to fill the tank completely = 5 + 5 + 26 = 36

∴ 36 minutes is required to fill the tank completely.

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