Question
Answers

39 people can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
(a) 10
(b) 13
(c) 14
(d) 15

Answer
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Hint: Use the unitary method to solve this question. Suppose the total amount of work would be ‘1’ (unity). Now, find the fraction of the amount done by 1 person in 1 working day with 1 hour a day to find the answer.

Complete step-by-step answer:
Let use the unitary method to calculate the part of work done by 1 person in one day and working in 1 hour by the following way:
Let us suppose the whole work as unity i.e. ‘1’.
So, 39 people in 12 days by working 5 hours a day are doing ‘1’ amount of 1 work.
So, 1 person in 12 days by working 5 hours in a day can do $'\dfrac{1}{39}'$ part of that work.
Hence, 1 person in 1 day by working 1 hour in a day can do $\dfrac{1}{39\times 12\times 5}$part of the work.
Now coming to the second condition of the problem, let us suppose 39 persons will complete the same work in ‘x’ days by working 6 hours a day.
So, 30 people in x days with 6 hours working in a day completes 1 work.
Hence, 1 person in 1 day with 1 hour working a day can complete the $\dfrac{1}{30\times x\times 6}$ part of the work.
Therefore, by using the both conditions, we get the same results i.e., part of working by 1 person in 1 day with 1 hour working. Hence, both should be equal.
So we get
$\Rightarrow$ $\dfrac{1}{30\times x\times 6}=\dfrac{1}{39\times 12\times 5}$
$\Rightarrow$ $30\times x\times 6=39\times 12\times 5$
$\begin{align}
  & x=\dfrac{39\times 12\times 5}{30\times 6} \\
 & x=\dfrac{39\times 2}{6}=\text{13 days} \\
\end{align}$
Hence, option (b) is the correct answer.

Note: One can use direct relation ${{M}_{1}}{{W}_{1}}{{D}_{1}}={{M}_{2}}{{W}_{2}}{{D}_{2}}$, where M is representing number of persons, W is representing working hours and D is representing number of days, ‘1’ and ‘2’ are used for two groups that complete the same work with ${{\text{M}}_{\text{1}}}{{\text{W}}_{\text{1}}}{{\text{D}}_{\text{1}}}\text{and}{{\text{M}}_{\text{2}}}{{\text{W}}_{\text{2}}}{{\text{D}}_{\text{2}}}$ features.
Hence, we can apply the given relation in these types of problems.
No need for formula if basics are clear for the chapter work and time. So, always think conceptually, you will be able to solve any problem from this chapter.