A pump usually fills a tank in 8 hours but due to a hole in the tank it took…
2025
A pump usually fills a tank in 8 hours but due to a hole in the tank it took 10 hours to fill the tank. How much time will it take the hole to drain the whole tank ?
- A.
25 hours
- B.
30 hours
- C.
35 hours
- D.
40 hours
Attempted by 16 students.
Show answer & explanation
Correct answer: D
Answer: 40 hours
Let T be the time (in hours) the hole takes to drain the whole tank. The pump fills at a rate of 1/8 tank per hour. With the hole open the tank is filled in 10 hours, so the net filling rate is 1/10 tank per hour.
Write the rate equation: pump rate − hole rate = net rate, i.e. 1/8 − 1/T = 1/10.
Rearrange to find the hole's rate: 1/T = 1/8 − 1/10 = (5 − 4)/40 = 1/40.
Invert to get the time: T = 40 hours.
Check: pump rate 1/8 minus hole rate 1/40 equals 5/40 − 1/40 = 4/40 = 1/10, which matches the observed net filling rate.