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.