# In a call centre $6$ employees working for $10$ hours complete a certain task. They started working at $11\,a.m.$. This continued till $5\,p.m.$ and after that, for each hour one more employee is added till the work gets completed. At what time will they complete the work

$

a)\,7:10\,p.m. \\

b)\,8:00\,p.m. \\

c)\,7:35\,p.m. \\

d)\,6:35\,p.m. \\

$

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**Hint:**$6$ employees do their work in $10$ hours. So $6$ employees can do $\dfrac{1}{{10}}$ job in $1$ hour.

$1$ Employee can do $\dfrac{1}{{6 \times 10}}$job in $1$hour.

So in this way you can solve this.

**Complete step-by-step answer:**

According to the question there is a work which can be done by $6$ employee in $10$ hours.

If the $6$ employee starts working at $11\,a.m.$ and continues till $5\,p.m.$ after that every hour one more employee is added till that work gets finished, so we have to find the time taken when work gets finished.

So it is given that

$6$ employees can complete the work in $10$ hours. So $6$ employees can do $\dfrac{1}{{10}}$ job in $1$ hour. And $1$ Employee can do $\dfrac{1}{{6 \times 10}}$ job in $1$ hour.

There we get the work of $1$ Employee can do $\dfrac{1}{{60}}$ jobs in $1$ hour.

Now, we are told that $6$ employees worked from $11\,a.m.$ to $5\,p.m.$ that means they worked for $6$ hours.

$6$ employees worked for $6$ hours, so total work they did $ = 6 \times 6 \times \dfrac{1}{{60}}$

As we know that $1$ employees do $\dfrac{1}{{60}}$ work in $1$ hour.

So $6$ employees in $6$ hours will do $ = \dfrac{{6 \times 6}}{{60}}$ work $ = \dfrac{6}{{10}}$ work

Now after $5\,p.m.$ one employee is added. So total now $7$ employee worked for $1$ hour that is $5\,p.m.\,\,to\,\,6\,p.m.$

So total work done by $7$ employees in one hour is $\dfrac{7}{{60}}$

So at $6\,p.m.$ the total work completed $ = \dfrac{6}{{10}} + \dfrac{7}{{60}} = \dfrac{{43}}{{60}}$ work.

Still some work is left

So one more employee is added, so total $8$ employees worked for one more hour $ = \dfrac{8}{{60}}$

So total work completed at $7\,p.m.\, = \dfrac{{43}}{{60}} + \dfrac{8}{{60}} = \dfrac{{51}}{{60}}$ work.

Still the work is left, so one more employee is added after $7\,p.m.$

Now the total no. of employees working becomes $9$ for $1$ hour that is $7\,p.m.\,\,\,to\,\,\,8\,p.m.$

So work done by $9$ employees in one hour $ = \dfrac{9}{{60}}$

Now at $8\,p.m.$ total work completed would be $ = \dfrac{{51}}{{60}} + \dfrac{9}{{60}} = \dfrac{{60}}{{60}} = 1$

Hence total work is completed at $8:00\,p.m.$

So option B is correct.

**Note:**We can use alternative method like

To complete the job $6 \times 10 = 60\,\dfrac{{man}}{{hour}}$

So from $11\,a.m.\,\,to\,\,5\,p.m.\, = 6 \times 6 = 36\,\,\dfrac{{man}}{{hour}}$ is done.

$

5\,p.m.\,\,to\,\,6\,p.m.\, = 7\,\dfrac{{man}}{{hour}} \\

6\,p.m.\,\,to\,\,7\,p.m.\, = 8\,\dfrac{{man}}{{hour}} \\

7\,p.m.\,\,to\,\,8\,p.m.\, = 9\,\dfrac{{man}}{{hour}} \\

$

So at $8\,p.m.\,$, how much work that is $\dfrac{{man}}{{hour}}$ is done $ = 36 + 7 + 8 + 9 = 60\dfrac{{man}}{{hour}}$ which is according to question. So, at $8\,p.m.\,$ the work gets completed.