Pipes M, N and S can fill a tank in 25, 50 and 100 minutes, respectively.…
2024
Pipes M, N and S can fill a tank in 25, 50 and 100 minutes, respectively. Initially, pipes N and S are kept open for 10 minutes, and then pipe N is shut while pipe M is opened. Pipe S is closed 15 minutes before the tank overflows. How much time (in minutes) will it take to fill the tank if the three pipes work in this pattern?
Answer: D. 27 — Determine Pipe Rates: Pipe M rate: 1/25 per minute. Pipe N rate: 1/50 per minute. Pipe S rate: 1/100 per minute. Analyze Time Phases: Phase 1 (First 10…
- A.
30
- B.
33
- C.
42
- D.
27
Show answer & explanation
Correct answer: D
Determine Pipe Rates:
Pipe M rate: 1/25 per minute.
Pipe N rate: 1/50 per minute.
Pipe S rate: 1/100 per minute.
Analyze Time Phases:
Phase 1 (First 10 minutes): Pipes N and S are open.
Work done = 10 * (1/50 + 1/100) = 10 * (3/100) = 0.3.
Phase 3 (Last 15 minutes): Only Pipe M is open.
Work done = 15 * (1/25) = 15 * (4/100) = 0.6.
Phase 2 (Remaining time): Let total time be T. Phase 2 duration is (T - 10 - 15) = (T - 25) minutes, during which pipes M and S are open.
Work done = (T - 25) * (1/25 + 1/100) = (T - 25) * (5/100) = 0.05 * (T - 25).
Solve for T:
Equation: 0.3 + 0.05 * (T - 25) + 0.6 = 1.
Solving this equation results in T = 27 minutes.