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?

Correct — A. Take the tank as 100 units, the LCM of 25, 50 and 100. Then M fills 4 units/min, N 2 and S 1.

Phase 1 — N and S together for 10 minutes:
(2 + 1) × 10 = 30 units, leaving 70.

Phase 3 is fixed by the wording — S is shut for the final 15 minutes, so M works alone:
4 × 15 = 60 units.

Phase 2 — M and S run at 4 + 1 = 5 units/min and must supply what is left:
70 − 60 = 10 units, so 10 ÷ 5 = 2 minutes.

Total = 10 + 2 + 15 = 27 minutes → option (a)

Why the others are wrong

• (b)
  42 — 42 overfills by a wide margin: N gives 20 units, S runs 27 minutes for 27 units and M runs 32 minutes for 128 units — 175 units poured into a 100-unit tank.
• (c)
  30 — 30 also overfills: N gives 20 units, S runs 30 − 15 = 15 minutes for 15 units and M runs 30 − 10 = 20 minutes for 80 units — 115 units, 15 more than the tank holds.
• (d)
  33 — 33 comes from forgetting the opening 10 minutes already delivered 30 units: 100 − 60 = 40 units at 5 units/min is 8 minutes, and 10 + 8 + 15 = 33, which plugged back delivers 130 units.

Pipes and cisterns is time-and-work with the tank as the job. Work in LCM units and every denominator disappears: set the tank at 100 units and the rates come out whole — M = 4, N = 2, S = 1 per minute.

The structural trick here is that the last phase is defined backwards. 'S is closed 15 minutes before the tank overflows' fixes the length of the final block without telling you when it starts.

So price that block first, subtract it and the known opening block, and the unknown middle stretch is the only thing left to solve for.

Key facts

• In LCM units the tank is 100: M = 4 units/min (25 min), N = 2 (50 min), S = 1 (100 min).
• The three phases deliver 30, 10 and 60 units, in 10, 2 and 15 minutes respectively.
• The tank fills at minute 27, and S is closed at minute 12.
• All three wrong options exceed 27 minutes, so plugging any of them back overfills the 100-unit tank.

Common traps

• Reading 'closed 15 minutes before the tank overflows' as 'closed 15 minutes after M is opened'.
• Forgetting that the opening 10 minutes have already delivered 30 units, which lands you on 33.
• Leaving N open past minute 10, or shutting M at the moment S is closed.

No directly related past PYQ was found.