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?
Question:
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?
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?
Options
Answer: (4) 27
Explanation:
M = 1/25 = 0.04 N = 1/50 = 0.02 S = 1/100 = 0.01 First 10 minutes: N + S open Contribution = 10 × (0.02 + 0.01) = 10 × 0.03 = 0.30 tank Then N is shut and M opened. Let the M + S phase last t minutes. Contribution = 0.05t S is closed 15 minutes before filling. Final 15 minutes only M runs: Contribution = 15 × 0.04 = 0.60 tank Total volume filled: 0.30 + 0.05t + 0.60 = 1 0.05t = 0.10 t = 2 minutes Total time = 10 + 2 + 15 = 27 minutes Answer = 27 minutes
Explanation:
M = 1/25 = 0.04 N = 1/50 = 0.02 S = 1/100 = 0.01 First 10 minutes: N + S open Contribution = 10 × (0.02 + 0.01) = 10 × 0.03 = 0.30 tank Then N is shut and M opened. Let the M + S phase last t minutes. Contribution = 0.05t S is closed 15 minutes before filling. Final 15 minutes only M runs: Contribution = 15 × 0.04 = 0.60 tank Total volume filled: 0.30 + 0.05t + 0.60 = 1 0.05t = 0.10 t = 2 minutes Total time = 10 + 2 + 15 = 27 minutes Answer = 27 minutes
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