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A contractor undertook a contract for a construction work to be completed in 180 days. He engaged 120 labours. But only 1/6th of the work was done in 1/5th of the scheduled time. The additional number of labours that will be required to complete the work in time, is

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A contractor undertook a contract for a construction work to be completed in 180 days. He engaged 120 labours. But only 1/6th of the work was done in 1/5th of the scheduled time. The additional number of labours that will be required to complete the work in time, is
1). 20
2). 40
3). 30
4). 15


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3 vote
Answered by on | Votes 3 |

Total Scheduled time = 180 days

1/5th of the scheduled time = 180/5 = 36 days

According to the given information,

120 labours can do 1/6th of the total work in 36 days

∴ remaining work = 5/6th of total work

$(\frac{{{M_1}{D_1}}}{{{W_1}}} = \frac{{{M_2}{D_2}}}{{{W_2}}})$

Where, M = Number of men, D = number of days, W = Amount of work

$(\Rightarrow \frac{{120 \times 36}}{{\frac{1}{6}}} = \frac{{{M_2}\; \times 144}}{{\frac{5}{6}}})$

⇒ M2 = 150

∴ Additional Labours required = 150 – 120 = 30

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