A contractor undertook to complete the work in 40 days and he deployed 20 men for his work. 8 days before the scheduled time he realised that `(1)/(3)rd` of the work was still to be done. How many more men were required to complete the work in stipulated time?

Options

A. 16
B. 15
C. 20
D. 25

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step 1: Understand the total work and initial conditions
The contractor has 40 days to complete the work and has deployed 20 men.

### Step 2: Calculate the total work done in 32 days
Since he realized 8 days before the scheduled time that 1/3 of the work was still to be done, it means he completed 2/3 of the work in the first 32 days.

### Step 3: Determine the amount of work done by 20 men in 32 days
Let the total work be represented as W. The work done in 32 days by 20 men can be calculated as:
\[ \text{Work done} = \text{Number of men} \times \text{Days} = 20 \text{ men} \times 32 \text{ days} \]
This means:
\[ \frac{2}{3} W = 20 \times 32 \]
\[ \frac{2}{3} W = 640 \]
To find W, we can rearrange the equation:
\[ W = 640 \times \frac{3}{2} = 960 \]

### Step 4: Calculate the remaining work
Since 1/3 of the work is still to be done, we can calculate:
\[ \text{Remaining work} = \frac{1}{3} W = \frac{1}{3} \times 960 = 320 \]

### Step 5: Determine the remaining time
There are 8 days left to complete the remaining work.

### Step 6: Calculate the number of men needed to complete the remaining work
Let X be the number of additional men required. The total number of men working now will be \( 20 + X \). The work done by these men in 8 days should equal the remaining work:
\[ (20 + X) \times 8 = 320 \]

### Step 7: Solve for X
Now we can solve the equation:
\[ 20 \times 8 + X \times 8 = 320 \]
\[ 160 + 8X = 320 \]
Subtracting 160 from both sides gives:
\[ 8X = 160 \]
Dividing both sides by 8 gives:
\[ X = 20 \]

### Conclusion
The contractor needs to hire 20 more men to complete the work on time.