A bathtub can be filled by the cold water faucet in 12 minutes and by the hot water faucet in 13 minutes. The drain can empty the tub in 5 minutes. Can the tub be filled if both faucets and the drain are open?
A) Yes
B) No

Question

Quizplus · Accepted Answer

Let the capacity of the bathtub be 156 units (LCM of 12, 13, and 5)
In one minute, the cold water faucet can fill 13 units (156/12) and the hot water faucet can fill 12 units (156/13).
So, in one minute both faucets together can fill 25 units (13+12).
But since the drain can empty the tub in 5 minutes, it can empty 31.2 units (156/5) in one minute.
Therefore, the net filling capacity per minute is -6.2 units (25-31.2)
Hence, the tub will not be filled and the answer is B.

A Bathtub Can Be Filled by the Cold Water Faucet