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Two pipes A and B can fill a tank in 32 minutes and 40 minutes. They worked together for 15 minutes, after that another outlet pipe C was opened and the tank took more 5 minutes to fill completely. In what time the outlet pipe C can empty the tank?
1. 40
2. 50
3. 35
4. 30

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Correct Answer - Option 1 : 40

Given:

Time taken by Pipe A to fill the tank = 32 minutes

Time taken by Pipe B to fill the tank = 40 minutes

Working time of (pipe A + pipe B) = 15 minutes

Working time of (pipe A + pipe B + pipe C) = 5 minutes

Calculation:

(Pipe A + Pipe B)’s 1 min’s work = (1/32) + (1/40)

= (5 + 4)/160

= 9/160

Time taken by (Pipe A + Pipe B) to finish the work = 160/9 minutes

(Pipe A + Pipe B)’s 15 min’s work = (9 × 15)/160

= 27/32

Work left = 1 – 27/32

= 5/32 unit

5/32 unit of work was finished by (pipe A + pipe B + pipe C) in 5 minutes.

∵ Total time to finish the work by (pipe A + pipe B + pipe C) = (5 × 32)/5

= 32 minutes

∴ Pipe C’s 1 min work = (pipe A + pipe B + pipe C)’s 1 min work - (Pipe A + Pipe B)’s 1 min work

= (1/32) – (9/160)

= (5 – 9)/160

= (-4)/160

= (-1)/40 unit

∴ Time taken by C to empty the tank is 40 minutes.

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