A contractor undertook to do a piece of work in 9 days. He employed certain number of laboures but 6 of them were absent from the very first day and the rest could finish the work in only 15 days. Find the number of men originally employed

Options

A. 15
B. 6
C. 13
D. 9

Answer

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

### Step 1: Define Variables
Let the total number of men originally employed be \( x \).

### Step 2: Calculate Total Work
The total work to be done can be expressed in terms of man-days. Since the contractor planned to complete the work in 9 days with \( x \) men, the total work is:
\[ \text{Total Work} = x \times 9 \text{ man-days} \]

### Step 3: Adjust for Absenteeism
Since 6 men were absent from the very first day, the number of men actually working is:
\[ \text{Men working} = x - 6 \]

### Step 4: Calculate Work Done by Remaining Men
The remaining men, \( x - 6 \), can complete the work in 15 days. Therefore, the total work done by these men can also be expressed as:
\[ \text{Total Work} = (x - 6) \times 15 \text{ man-days} \]

### Step 5: Set Equations Equal
Since both expressions represent the same total work, we can set them equal to each other:
\[ x \times 9 = (x - 6) \times 15 \]

### Step 6: Expand and Rearrange the Equation
Expanding the right side gives:
\[ 9x = 15x - 90 \]
Now, rearranging this equation:
\[ 90 = 15x - 9x \]
\[ 90 = 6x \]

### Step 7: Solve for \( x \)
Dividing both sides by 6 gives:
\[ x = \frac{90}{6} = 15 \]

### Conclusion
The number of men originally employed is \( \boxed{15} \).

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