Question

A contractor undertakes to do a piece of work in 36 days and employs 15 men to work 9 hours a day. But after 24 days, he finds that only 3/5 of the work is done. He then employs 3 more men. For how many hours a day should all the men work together to finish the work on time?​

Answer 1

Answer:

To finish the work, 18 men has to work for 10 hours a day.

Step-by-step explanation:

Given the number of days = 36

Number of men working = 15

Number of days worked = 24

Number of working hours per day = 9

Completed work = 3/5

Number of working hours in 24 days is $24\times 9=216\mbox{hours}$

15 men have done 3/5 work in 216 hours

15 men can do the whole work in

$216 \times \dfrac{5}{3} = 360 \mbox{hours}$

1 man can do the whole work in  360 x 15 = 5400 hours

Remained work is

$1-\dfrac{3}{5} = \dfrac{2}{5}$

1 man can do 2/5 of the work in

$= \dfrac{2}{5} \times 5400 = 2160\mbox{ hours}$

Given 3 more men have deployed to do the work.

Total men are 15 + 3 = 18

To complete the work each man has to work,

$\dfrac{ 2160}{18} = 120\mbox{ hours}$

Days left = 36 – 24 = 12 days  

Men required to complete the work in 12 days

So, number of hours to work a day is

$\dfrac{120}{12} = 10\mbox{hours}$

Therefore, to finish the work, 18 men has to work for 10 hours a day.

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