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 committed to constructing a road in \(200\) days with \(140\) workers.

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

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

The time remaining to complete the outstanding work is:
\( 200 - 60 = 140 \) days.

Let \( x \) represent the number of additional workers needed to finish the remaining work within the allocated time.
The governing formula is:

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

where:

• \( M \) denotes the number of workers.
• \( D \) represents the number of working days per week (assumed constant).
• \( T \) signifies the duration in weeks.
• \( W \) indicates the quantity of work.

Applying the formula to both phases:
Work completed in the initial \(60\) days by \(140\) individuals:

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

Cross-multiplying yields:

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

The left-hand side simplifies to:

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

The right-hand side is:

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

Equating both sides:

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

Dividing both sides by \(4\):

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

Multiplying both sides by \(3\):

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

Dividing both sides by \(140\):

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

Consequently,

\[x = 180 - 140 = 40\]

Therefore, \(40\) additional workers are required to complete the work on schedule.