2017 · Q39
A tap can fill a tub in 10 hours. After opening the tap for 5 hours it was found that a small outlet at the bottom of the tub was open and water was leaking through it. It was then immediately closed. It took 7 hours to fill the tub after closing the outlet. What time will be taken by the outlet to empty the full tub of water ?
Elementary MathematicsTime and Work
- A35 hours
- B25 hours
- C20 hours
- D17 hours
Explanation
The tap fills 1/10 of the tub per hour. In the first 5 hours with the leak open the tub reached 3/10 (since 7/10 was filled in the 7 hours after closing the leak). Net rate with leak = (3/10)/5 = 3/50 per hour, so the leak drains 1/10−3/50 = 1/25 of the tub per hour. A full tub empties in 25 hours. Hence option (B) 25 hours.