Question 68

# In a computer game, there are builders and destroyers. Together there are 20 of them.Some of them try to build a wall around 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 whenthere is no wall and the wall gets built in 3 hours, how many of them are destroyers?

Solution

Given, Builder + Destroyer = 20

Let total number of builders is $$'x'$$

therefore, number of destroyers $$= 20-x$$

Given,

$$1$$ Builder can build wall in $$15$$ hours

in $$1$$ hour $$1$$ builder can build $$=\frac{1}{15}$$ wall

in $$3$$ hour $$1$$ builder can build $$=3\ast\frac{1}{15}$$ wall

in $$3$$ hour $$x$$ builder can build $$=3\ast\frac{x}{15}$$ wall

Also given,

$$1$$ destroyer can demolish wall in $$10$$ hours

in $$1$$ hour $$1$$ destroyer can demolish $$=\frac{1}{10}$$ wall

in $$3$$ hour $$1$$ destroyer can demolish $$=3\ast\frac{1}{10}$$ wall

in $$3$$ hour $$20-x$$ destroyer can demolish $$=3\ast\frac{\left(20-x\right)}{10}$$ wall

according to question,

$$=3\ast\frac{1}{15}-3\ast\frac{\left(20-x\right)}{10}=1$$

$$x=14$$

therefore total number of destroyers $$= 20-x = 6$$