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      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?
      A 30 Correct Answer Incorrect Answer
      B 33 Correct Answer Incorrect Answer
      C 42 Correct Answer Incorrect Answer
      D 27 Correct Answer Incorrect Answer

      Solution

      Pipes M, N, and S fill the tank in 25, 50, and 100 minutes, respectively. Their rates are 1/25, 1/50, and 1/100 tank per minute. N and S fill in 10 minutes: Part filled = 10 × (1/50 + 1/100) = 10 × 3/100 = Remaining part: 1 – 3/10 = 7/10 Let x be the time taken after N is shut. For the last 15 minutes, only M works: Part filled by M in 15 minutes=15/25 = 3/5 Remaining part before the last 15 minutes: 7/10 – 3/5 = 7/10 – 6/10 = 1/10 Let t be the time when both M and S work: t × (1/25 + 1/100) = 1/10 t × 5/100 = 1/10  ⟹  t = 2 Total time: 10 + 2 + 15 = 27 minutes.

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