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In a computer game, a builder can build a wall in ten hours while a destroyer can demolish such a wall completely in fourteen hours. Both the builder and the destroyer were initially set to work together on the ground level, but, after 7 hours, the destroyer was taken out. What was the total time (in hours) taken to build the wall?

In a computer game, a builder can build a wall in ten hours while a destroyer can demolish such a wall completely in fourteen hours. Both the builder and the destroyer were initially set to work together on the ground level, but, after 7 hours, the destroyer was taken out. What was the total time (in hours) taken to build the wall? Correct Answer 15

Let the total work required to build a wall be 70 units (LCM of 10 and 14).

⇒ Work done by a builder in 1 hour = 70/10 = 7 units.

⇒ Work done by destroyer in 1 hour = 70/-14 = -5 units.

⇒ Total work done in 1 hour = 7 – 5 = 2 units

Work done by both of them = 2 × 7 = 14 units

Remaining work = 70 - 14 = 56 units

Remaining work was done by the builder.

∴ Time required = 56/7 = 8 hours

Total time required = 8 + 7 = 15 hours

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