If 3 pipes named as A, B, C. Pipes A and B can fill a tank in 6 and 5 hours…
2023
If 3 pipes named as A, B, C. Pipes A and B can fill a tank in 6 and 5 hours respectively. Pipe C can empty it in 18 hours. If all the three pipes are turned on together, then the tank will be filled in:
- A.
12/90 hrs
- B.
7/45 hrs
- C.
14/45 hrs
- D.
12/45 hrs
Attempted by 33 students.
Show answer & explanation
Correct answer: C
Solution: Find the net filling rate and then take its reciprocal to get the time.
Individual rates (tank per hour): A = 1/6, B = 1/5, C = -1/18 (emptying is negative).
Sum the rates: 1/6 + 1/5 - 1/18. Use common denominator 90: 15/90 + 18/90 - 5/90 = 28/90 = 14/45.
This 14/45 is the net filling rate (tank per hour). The time to fill = 1 ÷ (14/45) = 45/14 hours.
As a mixed number or decimal: 45/14 = 3 3/14 ≈ 3.214 hours.
Common mistake: Confusing the net rate (14/45 tank/hour) with the time. Remember to take the reciprocal of the net rate to find the time.