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Tap A alone can fill the tank in 30 hours while tap B alone can fill the tank in 12 hours. Tap C empties the filled tank. When all three taps are opened then the tank gets emptied in 20 hours. In what time the tank gets emptied when Tap C is opened after 1/4th of the tank is filled by tap A and tap B?

Tap A alone can fill the tank in 30 hours while tap B alone can fill the tank in 12 hours. Tap C empties the filled tank. When all three taps are opened then the tank gets emptied in 20 hours. In what time the tank gets emptied when Tap C is opened after 1/4th of the tank is filled by tap A and tap B? Correct Answer 1 hour and 30 minutes

Given:

Tap A's 1 hour's work = 1/30

Tap B's 1 hour's work = 1/12

Calculation:

Let tap C's 1 hour's work be 1/C.

Tap (A + B + C)’s 1 hours work = 1/30 + 1/12 – 1/C = 7/60 – 1/C = (7C – 60)/60C

Then,

⇒ 60C/(7C – 60) = -20

⇒ 3C = -7C + 60

⇒ C = 6

Tap C alone can empty the tank in 6 hours.

∴ Time taken by tap C to empty the 1/4th tank = ¼ × 6 = 3/2 = 1 + ½ = 1 hour and 30 minutes 

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