Pipe A can fill an empty cistern alone in 17 hours and pipe B can fill the…
2025
Pipe A can fill an empty cistern alone in 17 hours and pipe B can fill the same cistern
alone in 23 hours. The time taken by them to fill half of the cistern by operating together
will be:
- A.
\(8\frac{71}{80}\) hours
- B.
\(10\frac{71}{80}\) hours
- C.
\(4\frac{71}{80}\) hours
- D.
\(2\frac{71}{80}\) hours
Attempted by 2 students.
Show answer & explanation
Correct answer: C
Concept
When two pipes work together, their filling rates (work per hour) add up: combined rate = rate of A + rate of B. The time to complete a given fraction of the work is that fraction divided by the combined rate (equivalently, the full-tank time multiplied by that fraction).
Application
Pipe A’s rate = 1/17 of the cistern per hour; Pipe B’s rate = 1/23 of the cistern per hour.
Combined rate = 1/17 + 1/23 = (23 + 17)/(17 × 23) = 40/391 of the cistern per hour.
Time to fill the FULL cistern together = 391/40 hours.
Time to fill HALF the cistern together = (391/40) × (1/2) = 391/80 hours.
391/80 = 4 remainder 71, so 391/80 hours = \(4\frac{71}{80}\) hours.
Cross-check
Multiply the combined rate by this time and confirm it gives exactly half the cistern: (40/391) × (391/80) = 40/80 = 1/2. This matches the half-cistern requirement, confirming the working.