2019 · Q79
Two taps X and Y are fixed to a water tank. If only X is opened, it drains out the full tank of water in 20 minutes. If both X and Y are opened, then they drain out the full tank of water in 15 minutes. If only Y is opened, how long does it take to drain out the full tank of water?
Elementary MathematicsTime and Work
- A30 minutes
- B45 minutes
- C60 minutes
- D90 minutes
Explanation
This is a rate-addition (work–time) problem: if Y alone drains the tank in T minutes, the combined rate is 1/20 + 1/T tank per minute. Together they empty the tank in 15 minutes, so 1/20 + 1/T = 1/15. Rearranging gives 1/T = 1/15 − 1/20 = (4 − 3)/60 = 1/60, hence T = 60 minutes. Hence option (c). The distractor 30 minutes comes from wrongly subtracting rates (1/15 − 1/20 treated as difference of times), and 45/90 from halving or doubling errors.