Question

A contractor agreed to construct a 6 km road in 200 days. He employed 140 persons for the work. After 60 days, he realized that only 1.5 km road has been completed. How many additional people would he need to employ in order to finish the work exactly on time?

Answer 1

	Men	Tunnel	Days
Initial	140	1.5 km	60
Remaining	X	4.5 km	140

\(X = 140×\frac{4.5}{1.5}×\frac{60}{140} = 180\)

Additional men required = \(180-140 = 40\)

Answer 2

A contractor agreed to build a road in \(200\) days and had \(140\) persons to do  work.
After \(60\) days, only \(\frac 14^{th}\) of the road could be build.
We know that,
\(\frac {M_1 × D_1 × T_1}{W_1}= \frac {M_2 × D_2 × T_2}{W_2}\)
Amount of work remaining \(= 1-\frac 14 = \frac 34\) unit of work.
Number of days in which the remaining work needs to be completed \(= 200 - 140 = 60\) days.
Let \(x \) persons be extra needed to finish the work.

\(\frac {140 × 60}{\frac 14}= \frac {(140 + x) × 140}{\frac 34}\)

\(4 × 60= \frac {(140 + x) × 4}{3}\)
\(140+x=180\)
\(x=180-140\)
\(x=40\)

So, the answer is \(40\).