Question

A job can be completed by 12 men in 12 days. How many extra days will be needed to complete the job, if 6 men leave after working for 6 days?
$\left( a \right)$ 10 days
$\left( b \right)$ 12 days
$\left( c \right)$ 6 days
$\left( d \right)$ 24 days

Answer 1

Hint: In this particular question use the concept that if 12 men can do a work in 12 days so the 1 day work of 12 men is $\dfrac{1}{{12}}$, therefore one day work of 1 man is $\dfrac{1}{{12 \times 12}}$,so the 6 day work of 12 men is $\dfrac{{6 \times 12}}{{12 \times 12}} = \dfrac{1}{2}$, so use these concept to reach the solution of the question.

Complete step-by-step answer:
Given data:
A job can be completed by 12 men in 12 days.
Now we have to find out how many extra days will be needed to complete the job, if 6 men leave after working for 6 days.
Let the work = 1
Now as the work is completed in 12 days by 12 men.
So the 1 day work of 12 men = $\dfrac{1}{{12}}$.
So the 1 day work of 1 man = $\dfrac{1}{{12 \times 12}}$
So the 6 day work of 1 man = $\dfrac{6}{{12 \times 12}}$.

So the 6 day work of 12 men = $\dfrac{{6 \times 12}}{{12 \times 12}} = \dfrac{1}{2}$.
So the remaining work after 6 days work of 6 men = total work – 6 day work of 12 men.
Therefore, the remaining work after 6 days work of 6 men = 1 – $\dfrac{1}{2}$ = $\dfrac{1}{2}$
So $\dfrac{1}{2}$ work is remaining.
Now after 6 days 6 workers go on leave, so the remaining work is done by the remaining 6 workers.
Let the number of days taken by remaining 6 workers be X.
So, the 12 men can complete 1 work in 12 days which is equal to 6 men can complete $\dfrac{1}{2}$work in X days.
Therefore, $\dfrac{1}{{12 \times 12}} = \dfrac{{\dfrac{1}{2}}}{{6 \times x}}$
Now simplify it we have,
$ \Rightarrow 6x = \dfrac{1}{2}\left( {144} \right)$
$ \Rightarrow x = \dfrac{{72}}{6} = 12$ days.
So the total number of days to finish the work this time = 12 + 6 = 18 days
So the number of extra days which is needed to complete the work = 18 – 12 = 6 days.
Hence option (c) is the correct answer.

Note: Whenever we face such types of questions the key concept we have to remember is that always recall that 12 men can complete 1 work in 12 days which is equal to the 6 men can complete $\dfrac{1}{2}$work in X days, so just covert this information into equation as above and simplify we will get the number of days in which the remaining work is finished, so the total work is finished is the sum of the previous days in which all 12 workers working and the number of days in which 6 workers are working so the extra number of days is the difference of current scenario days in which total work is finished into two parts and the number of days in which total work is finished in only one part.