Question 33

# 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 level ground. But after 7 hours the destroyer was taken out. What was the total time (in hours) taken to build the wall?

Solution

Work done by builder in 1 hour isÂ  Â  Â  Â  Â  Â  Â  Â  =Â Â $$\frac{1}{10}$$ unit

Work demolished by destroyer in 1 hour isÂ Â  =Â $$\frac{1}{14}$$ unit

Net work done by both of them in 1 hour isÂ  =Â $$\frac{1}{10}-\frac{1}{14}=\frac{\left(7-5\right)}{70}=\frac{2}{70}=\frac{1}{35}$$ unit

Work done by them in 7 hoursÂ  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  =Â $$7\times\frac{1}{35}= \frac{1}5$$ unit

Work left after 7 hoursÂ  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â =Â $$1-\frac{1}{5}=\frac{4}{5}$$ unit

Let time taken by builder to complete remaining work =Â t hours.

ACT

$$t\times\frac{1}{10} = \frac{4}{5}$$

$$\frac{4}{5}\times\frac{10}{1} = 8 hours$$

Total time taken isÂ $$7+8=15$$ hours.

Hence Option (B) is right answer.