A contractor undertakes to make a road in 40 days and employs 25 men. After 24 days, he finds that only onethird of the road is made. How many extra men should he employ so that he is able to complete the work 4 days earlier?

Options

A. 100
B. 60
C. 75
D. None of these

Answer

To solve the problem step by step, we will follow a structured approach:

### Step 1: Understand the Problem
The contractor has 40 days to complete a road with 25 men. After 24 days, only one-third of the road is completed. He needs to finish the remaining two-thirds of the road in 36 days (4 days earlier than planned).

**Hint:** Break down the total work into fractions to understand how much is left and how much time is available.

### Step 2: Calculate the Work Done
In 24 days, 25 men completed one-third of the road.

Let the total work be represented as W.
- Work done in 24 days = \( \frac{1}{3}W \)

**Hint:** Use the formula for work done: Work = Number of men × Number of days.

### Step 3: Calculate the Remaining Work
The remaining work is:
- Remaining work = Total work - Work done = \( W - \frac{1}{3}W = \frac{2}{3}W \)

**Hint:** Always check how much work is left after a certain period.

### Step 4: Determine the Time Left
The contractor now has 36 days to complete the remaining work.

**Hint:** Keep track of the time constraints to ensure the work can be completed on schedule.

### Step 5: Set Up the Equation
Let \( x \) be the number of extra men to be employed. The total number of men after hiring extra men will be \( 25 + x \).

The equation using the work formula is:
\[ (25 + x) \times 36 = \frac{2}{3}W \]

From the first part, we know:
\[ 25 \times 24 = \frac{1}{3}W \implies W = 25 \times 24 \times 3 = 1800 \]

Now substitute \( W \) into the equation:
\[ (25 + x) \times 36 = \frac{2}{3} \times 1800 \]

**Hint:** Substitute known values to simplify the equation.

### Step 6: Simplify the Equation
Calculate \( \frac{2}{3} \times 1800 \):
\[ \frac{2}{3} \times 1800 = 1200 \]
So the equation becomes:
\[ (25 + x) \times 36 = 1200 \]

**Hint:** Always simplify your calculations to make the problem easier to solve.

### Step 7: Solve for \( x \)
Now divide both sides by 36:
\[ 25 + x = \frac{1200}{36} = 33.33 \]
Now, subtract 25 from both sides:
\[ x = 33.33 - 25 = 8.33 \]

Since \( x \) must be a whole number, we round up to the nearest whole number:
\[ x = 9 \]

**Hint:** When dealing with people, always round up to ensure you have enough workers.

### Step 8: Conclusion
The contractor needs to hire 9 extra men to complete the work in 36 days.

**Final Answer:** The contractor should employ **9 extra men**.