Given: Time is taken by worker A to construct wall = 10 hours Time is taken by worker B to construct wall = 20 hours Time is taken by worker C to destroy wall = 5 hours Formula used: Time = Total work/Efficiency Calculation: Let the total amount of work done in constructing a wall be 20 units (L.C.M of 5, 10, and 20) Hence, work done by A in one hour = 20/10 = 2 units Work done by B in one hour = 20/20 = 1 unit Work done by C in one hour = -20/5 = -4 units ⇒ Now, when A and B work together, work done by them in one hour is 2 + 1 = 3 units They together work for 6 hours, therefore work done in 6 hours = 3 × 6 = 18 units After 6 hours C joins them, work done by A, B and C in one hour = 2 + 1 - 4 = -1 unit Time taken to nullify 27 units of work will be x hours, ⇒ 18 + x(-1) = 0 ⇒ x = 18 hours ∴ The time is taken to destroy the wall is 18 hours Shortcut Trick [ alt="vikashhh" src="//storage.googleapis.com/tb-img/production/21/02/vikashhh.PNG" style="width: 476px; height: 129px;"> Worker C will do the negative work of 4 units Work done by A and B together in 6 hours = (2 + 1) × 6 = 18 units When all the three workers do the work = (2 + 1) – 4 = -1 unit ! unit is destroyed in 1 hour, so time is taken to destroy 18 units = 18/1 = 18 hours ∴ The time is taken to destroy the wall is 18 hours