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 `1/2`th of the work was still to be done. How many more men were required.to complete the work in stipulated time?

Options

A. 60
B. 80
C. 20
D. 25

Answer

To solve the problem step by step, we will follow the logic laid out in the video transcript.

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

**Hint:** Remember that the total work can be represented as a unit of work that needs to be completed.

### Step 2: Calculate the amount of work done in the initial period
The contractor has been working for 32 days (40 days - 8 days remaining). In this time, he has completed half of the work.

**Hint:** If half of the work is done in 32 days, then the remaining half must be completed in the remaining 8 days.

### Step 3: Determine the work left to be done
Since half of the work is completed, there is still 1 unit of work left to be done in the remaining 8 days.

**Hint:** Think about how much work needs to be done in the remaining time.

### Step 4: Calculate the work rate of the initial workforce
The initial workforce of 20 men completed 1 unit of work in 32 days. Therefore, the work rate of 20 men can be calculated as follows:
- Work done by 20 men in 32 days = 1 unit
- Work done by 1 man in 32 days = 1/20 units
- Work done by 1 man in 1 day = 1/(20 * 32) = 1/640 units

**Hint:** Consider how many units of work one man can do in one day.

### Step 5: Determine the work rate needed to complete the remaining work
To complete the remaining 1 unit of work in 8 days, we need to find out how many men (let's call this number X) are required:
- Work required per day = 1 unit / 8 days = 1/8 units per day

**Hint:** Set up an equation based on the work rate needed to complete the remaining work.

### Step 6: Set up the equation for the number of men required
The work done by X men in one day should equal the required work per day:
\[ X \times \frac{1}{640} = \frac{1}{8} \]
To find X, multiply both sides by 640:
\[ X = 640 \times \frac{1}{8} = 80 \]

**Hint:** Make sure to isolate X to find the total number of men needed.

### Step 7: Calculate the additional men required
The contractor initially had 20 men. Now he needs 80 men to complete the work on time. Therefore, the additional number of men required is:
\[ 80 - 20 = 60 \]

**Hint:** Subtract the initial number of men from the total number of men needed to find out how many more are required.

### Final Answer
The contractor needs **60 more men** to complete the work in the stipulated time.

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