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?

# 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?

1. A
$13$
2. B
$14$
3. C
$15$
4. D
$10$

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### Solution:

Concept- Time and work share a fundamental idea in common with other arithmetic topics, namely the idea of proportionality. When the amount of work is constant, efficiency is inversely proportional to the length of time required.
Finding the required time for 30 persons, working 6 hours a day by unitary method.
Given as we know,
39 people can repair a road in 12 days, working 5 hours a days suppose the whole work is 1
Now,
39 people in 12 days by working 5 hours in a day $=\frac{1}{39}$
Hence,
One person in a day by working 1 hour
Now,
Suppose 39 person done their in x days $=\frac{1}{30×x×6}$
$=\frac{1}{30×x×6}=\frac{1}{39×12×5}$
$=30×x×6=39×12×5$
$x=\frac{39×12×5}{30×6}$

Hence, the correct option is 1) 13 days.

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