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In a computer game, there are builders and destroyers. Together there are 20 of them. Some of them try to build a wall around a castle while the rest try to demolish it. Each of the builders can build the wall alone in 15 hours while any of the destroyers can demolish it in 10 hours. If all 20 builders and destroyers are made active when there is no wall and the wall get built in 3 hours, how many of them are destroyers?

In a computer game, there are builders and destroyers. Together there are 20 of them. Some of them try to build a wall around a castle while the rest try to demolish it. Each of the builders can build the wall alone in 15 hours while any of the destroyers can demolish it in 10 hours. If all 20 builders and destroyers are made active when there is no wall and the wall get built in 3 hours, how many of them are destroyers? Correct Answer 6

Let the total work be 30 units, (LCM of 15 and 10)

Each of the builders can build the wall alone in 15 hours while any of the destroyers can demolish it in 10 hours, and when they work together the wall gets built in 3 hours,

⇒ 1 hour work of Builder and Destroyer = 30/3 = 10 units

⇒ 1 hour work of Builder = 30/15 = 2 units

⇒ 1 hour work of Destroyer = 30/10 = -3 units

⇒ Difference between the work done = 10

Let the number of destroyers be x and number of builders be (20 – x),

⇒ 2(20 – x) – 3x = 10

⇒ x = 6

∴ Number of destroyers is 6.

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