A contractor undertook to finish a road 12 km long in 350 days. But after employing 45 men for 200 days, he fo

Question

A contractor undertook to finish a road 12 km long in 350 days. But after employing 45 men for 200 days, he found that only 4 km of the road had been built. How many additional men must be engaged to finish the work in the given time?

Accepted Answer

Let's define the initial scenario parameters:
*

M_{1} = 45

men
*

D_{1} = 200

days
*

W_{1} = 4 km

Remaining work parameters:

* Remaining work length

W_{2} = 12 - 4 = 8 km

* Remaining time duration

D_{2} = 350 - 200 = 150

days
* Let total men required for the remaining period be

M_{2}

Using the formula

\frac{M _{1} D _{1}}{W _{1}} = \frac{M _{2} D _{2}}{W _{2}}

:

\frac{45 \times 200}{4} = \frac{M _{2} \times 150}{8}

\frac{45 \times 200}{1} = \frac{M _{2} \times 150}{2}

9000 = 75 \times M_{2}

M_{2} = \frac{9000}{75} = 120 men

Additional men required = M_{2} - M_{1} = 120 - 45 = 75 men

A contractor undertook to finish a road $12 km$ long in $350$ days. But after employing $45$ men for $200$ days, he found that only $4 km$ of the road had been built. How many additional men must be engaged to finish the work in the given time?

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A contractor undertook to finish a road 12km long in 350 days. But after employing 45 men for 200 days, he found that only 4km of the road had been built. How many additional men must be engaged to finish the work in the given time?