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? [This Question was asked as TITA] 

• A. 10
• B. 40
• C. 50
• D. 60

Answer 1

The Correct Option is B

A contractor agreed to build a road in \(200\) days using \(140\) workers.

After \(60\) days, only \(\frac{1}{4}\) of the road was completed. 

This means the remaining work is: 
\(1 - \frac{1}{4} = \frac{3}{4}\)

The number of days left to complete the remaining work is: 
\(200 - 60 = 140\) days

Let \(x\) be the number of extra workers required to complete the remaining work on time. 
We will use the formula: 
 

\[\frac{M_1 \times D_1 \times T_1}{W_1} = \frac{M_2 \times D_2 \times T_2}{W_2}\]

 where:

• \(M\) = number of workers
• \(D\) = number of working days per week (assume constant)
• \(T\) = number of weeks
• \(W\) = amount of work

 

Applying the formula for both phases: 
Work done in first 60 days by 140 persons: 

\[\frac{140 \times 60}{\frac{1}{4}} = \frac{(140 + x) \times 140}{\frac{3}{4}}\]

Multiply both sides: 
 

\[140 \times 60 \times 4 = (140 + x) \times 140 \times \frac{4}{3}\]

Simplifying LHS: 

\[140 \times 60 \times 4 = 33600\]

 
RHS: 

\[\frac{4}{3} \times 140 \times (140 + x)\]

Now equate both sides: 
 

\[33600 = \frac{4}{3} \times 140 \times (140 + x)\]

Divide both sides by 4: 

\[8400 = \frac{1}{3} \times 140 \times (140 + x)\]

Multiply both sides by 3: 

\[25200 = 140 \times (140 + x)\]

Divide both sides by 140: 

\[\frac{25200}{140} = 140 + x \Rightarrow 180 = 140 + x\]

Therefore, 

\[x = 180 - 140 = 40\]

So, 40 extra workers are required to finish the work on time.