# Two taps A and B can fill a tank in 12 minutes and 15 minutes respectively. The tank can be emptied by a third tap C in 6 minutes. If A and B are kept

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Two taps A and B can fill a tank in 12 minutes and 15 minutes respectively. The tank can be emptied by a third tap C in 6 minutes. If A and B are kept open for 5 minutes in the beginning and then C is opened along with A and B being kept open, the time taken to empty the tank is:
1. 60 minutes
2. 45 minutes
3. 30 minutes
4. 75 minutes

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Correct Answer - Option 2 : 45 minutes

Given:

Tap A can fill the tank in 12 minutes

The tap B can fill the tank in 15 minutes

The tap C can empty the tank in 6 minutes

Calculation:

⇒ One minutes work of A and B = (1/12 + 1/15) = 3/20

⇒ 5 minutes work of A and B = 5 × (3/20) = 3/4

⇒ The one minutes of work of A, B, and C = (1/12 + 1/15 - 1/6) = -1/60

⇒ Time taken when all three tap opened = (3/4) × (60) = 45 minutes

∴ The required result will be 45 minutes.