Question

160 people are employed to finish the work in 120 days. After 40 days it was found that only \(\frac{1}{5}\) of the work is completed. To complete the work in the scheduled time, how many more people are to be employed?

• A. 40
• B. 80
• C. 120
• D. 160

Hint:

Always identify the remaining work and remaining time correctly before setting up the equation for the second phase of the project.

Answer 1

The Correct Option is D

Concept: This problem uses the work-days relationship formula: \(\frac{M_1 \times D_1}{W_1} = \frac{M_2 \times D_2}{W_2}\), where \( M \) is the number of workers, \( D \) is the number of days, and \( W \) is the fraction of work completed.

Step 1: Analyze the initial work phase.
Given: \( M_1 = 160 \), \( D_1 = 40 \), \( W_1 = \frac{1}{5} \).

Step 2: Determine the requirements for the remaining work.
Remaining work (\( W_2 \)) = \( 1 - \frac{1}{5} = \frac{4}{5} \). Remaining time (\( D_2 \)) = \( 120 - 40 = 80 \) days.

Step 3: Apply the formula to find the total workers needed (\( M_2 \)).
\[ \frac{160 \times 40}{1/5} = \frac{M_2 \times 80}{4/5} \] \[ 160 \times 40 \times 5 = M_2 \times 80 \times \frac{5}{4} \] \[ 32000 = M_2 \times 100 \implies M_2 = 320 \]

Step 4: Calculate additional workers.
\[ \text{Additional workers} = M_2 - M_1 = 320 - 160 = 160 \] \centerline{{160}}