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A bathtub can be filled by 2 inlet pipes in 10 minutes and 15 minutes respectively. A person leaves the tub after opening both the pipes simultaneously and returns at the moment when the tub is expected to get filled. He finds that the drainage pipe was also open so he now closes it. In 3 minutes more, the tub gets filled. What will be the time taken by the drainage pipe to empty a completely filled tub?

A bathtub can be filled by 2 inlet pipes in 10 minutes and 15 minutes respectively. A person leaves the tub after opening both the pipes simultaneously and returns at the moment when the tub is expected to get filled. He finds that the drainage pipe was also open so he now closes it. In 3 minutes more, the tub gets filled. What will be the time taken by the drainage pipe to empty a completely filled tub? Correct Answer 12 minutes

Suppose the capacity of the bathtub be 30 units (LCM of 10 and 15)

⇒ Efficiency of 1st pipe = 30/10 = 3

⇒ Efficiency of 2nd pipe = 30/15 = 2

Suppose the efficiency of drainage pipe = x

⇒ Time in which the tub will be filled = 30/ (3 + 2) = 6 minutes

Since the drainage pipe is opened after 6 minutes

⇒ Water emptied by the drainage pipe in 6 minutes will be filled by two inlet pipes in 3 more minutes

⇒ 6x = (3 + 2) × 3

⇒ 6x = 15

⇒ x = 15/6

⇒ Efficiency of drainage pipe = 15/6

∴ Time taken by the drainage pipe to empty the tub = 30/ (15/6) = 12 minutes

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