A contractor undertakes to make a mall in 60 days and he
employs 30 men. After 30 days it is found that only one-
third of the work is completed. How many extre men should
he employ so that the work is completed on time?

Options

A. 20 men
B. 25 men
C. 30 men
D. 40 men

Explanation

To solve the problem, we will follow these steps:

### Step 1: Determine the total work in terms of man-days.
The contractor has 60 days to complete the work with 30 men. Therefore, the total work (W) can be calculated as:
\[ W = \text{Number of men} \times \text{Number of days} = 30 \text{ men} \times 60 \text{ days} = 1800 \text{ man-days} \]

### Step 2: Calculate the work completed in the first 30 days.
After 30 days, it is found that only one-third of the work is completed. Thus, the work completed (W_completed) is:
\[ W_{\text{completed}} = \frac{1}{3} W = \frac{1}{3} \times 1800 = 600 \text{ man-days} \]

### Step 3: Determine the remaining work.
The remaining work (W_remaining) after 30 days is:
\[ W_{\text{remaining}} = W - W_{\text{completed}} = 1800 - 600 = 1200 \text{ man-days} \]

### Step 4: Calculate the remaining time to complete the work.
Since 30 days have already passed, the remaining time (T_remaining) is:
\[ T_{\text{remaining}} = 60 - 30 = 30 \text{ days} \]

### Step 5: Determine the number of men needed to complete the remaining work on time.
To find the number of men (M_needed) required to complete the remaining work in the remaining time, we can use the formula:
\[ M_{\text{needed}} = \frac{W_{\text{remaining}}}{T_{\text{remaining}}} = \frac{1200 \text{ man-days}}{30 \text{ days}} = 40 \text{ men} \]

### Step 6: Calculate the extra men needed.
The contractor originally employed 30 men, so the extra men (E) needed are:
\[ E = M_{\text{needed}} - \text{Original men} = 40 - 30 = 10 \text{ men} \]

### Conclusion:
The contractor needs to employ **10 extra men** to complete the work on time.

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