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Question:

A and B can completely build a wall in 20 and 30 days respectively while C can demolish the entire wall in 60 days. If A, B and C work one after the other starting with A, then B and then C. On which day from the start will the work get completed.

Explanation:

Let the work to be done = LCM (20, 30, 60) = 60 units.

Efficiency of A = 60/20 = 3 units/day
Efficiency of B = 60/30 = 2 units/day
Efficiency of C = 60/60 = -1 units/day

Since they work on alternate days, they would work in cycles of 3 days.

Work done by A on first day of the cycle = 3 units
Work done by B on second day of the cycle = 2 units
Work done by C on third day of the cycle = -1 units

Work done in 1 cycle = 3 + 2 - 1 = 4 units

Number of cycles required = 60/4 = 15 cycles.

Now since work done by C is negative we need to analyse last couple of cycles.

Work done by the end of 13 cycles (39 days) = 13 × 4 = 52.

Work done in 14^th cycle:
on 40^th day = 3. Total work done = 3 + 52 = 55
on 41^st day = 2. Total work done = 2 + 55 = 57
on 42^nd day = -1. Total work done = -1 + 57 = 56

Work done in 15^th cycle:
on 43^rd day = 3. Total work done = 3 + 56 = 59
on 44^th day = 2. Total work done = 2 + 59 = 61

Hence, the wall gets built on 44^th day itself.

Hence, 44.

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