SSC MTS 2 Aug 2019 Shift 1 Paper

Given:
Time taken by A to fill tank = 6 hours
Time taken by B to fill tank = 8 hours
Time taken by A, B and, C together to fill the tank = 12 hours
Concept used:
Total work = time × efficiency
Calculation:
Let the capacity of the tank ( work to be done) be 24x units (LCM of 6, 8, 12)
⇒ The efficiency of pipe A = 24x/6 = 4x units/day
⇒ Efficiency of pipe B = 24x/8 = 3x units/day
⇒ Efficiency of pipe (A + B + C) = 24x/12 = 2x units/day
⇒ Efficiency of pipe C = efficiency of (A + B = C) - efficiency of (A + B)
Efficiency of pipe C = 2x – (4x + 3x) = – 5x units/day
Negative efficiency implies that pipe C is emptying pipe.
⇒ Time taken by pipe C to empty the filled tank = 24x/5x
= 4.8 hours or 4 hrs 48 min
∴ The pipe C will empty the tank in 4 hrs 48 mins.