A contractor undertook to do a certain piece of work in 18 days. He employed certain number of men but 12 of them being absent from the very 1st day , the rest could finish the work in 30 days . Find the number of men originally employed .

Options

A. 40
B. 15
C. 45
D. 30

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Define Variables
Let \( X \) be the number of men originally employed by the contractor.

### Step 2: Work Done Calculation
The total work can be expressed in terms of men and days. If \( X \) men can complete the work in 18 days, the total work \( W \) can be expressed as:
\[ W = X \times 18 \]

### Step 3: Adjust for Absenteeism
Since 12 men were absent from the first day, the number of men actually working is \( X - 12 \). These remaining men completed the work in 30 days. Therefore, the work done by these men can be expressed as:
\[ W = (X - 12) \times 30 \]

### Step 4: Set the Two Expressions for Work Equal
Since both expressions represent the same total work \( W \), we can set them equal to each other:
\[ X \times 18 = (X - 12) \times 30 \]

### Step 5: Expand and Rearrange the Equation
Expanding the right side:
\[ 18X = 30X - 360 \]
Now, rearranging the equation to isolate \( X \):
\[ 18X - 30X = -360 \]
\[ -12X = -360 \]

### Step 6: Solve for \( X \)
Dividing both sides by -12:
\[ X = \frac{360}{12} = 30 \]

### Conclusion
Thus, the number of men originally employed by the contractor is \( \boxed{30} \).

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