Finding the time taken to complete the work

Question

In a call centre, $6$ employees working for ten hours can complete a certain task. They started working at 11 am .They continued till 5 pm. After that, each hour one more employee is added till the work gets completed. At what time will the work complete?

Answer 1

So you know that 1 employee working for 1 hour completes $1/60$ 'th of the task.

• At the beginning $6$ employees work for $6$ hours. They complete $36/60$ of the task.

• Then $7$ employees work for $1$ hour. This makes the task being completed at $43/60$.

• Then $8$ employees work for $1$ hour. This makes the task being completed at $51/60$.

• ...

Can you finish from here ?

Answer 2

Till 5 p.m. 60 percent ($=\frac{6}{10}=\frac{36}{60}$) of the work is done, because they have worked 6 hours and every hour they finish $\frac1{10}$ of the work.

The next hour they finish $\frac76\cdot \frac1{10}$ of the work, because there are 7 workers instead of 6 workers.

The next hour they finish $\frac86\cdot \frac1{10}$ of the work, because there are 8 workers instead of 6 workers.

You sum up the three proportions and check if the result is $1$. If not go on in the same way.