Some mans promised to do a work in 10 days but 8 of them were absent and remaining did the work in 18 days. What was the original number of mans?

Options

A. 10
B. 21
C. 15
D. 18

Answer

To solve the problem, we need to find the original number of men who promised to complete the work in 10 days. Let's break it down step by step.

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

### Step 2: Calculate the Total Work
The total work can be calculated based on the number of men and the number of days they promised to work. If \( x \) men can complete the work in 10 days, the total work (in man-days) is:
\[ \text{Total Work} = x \times 10 \]

### Step 3: Calculate Work Done by Remaining Men
Since 8 men were absent, the number of men who actually worked is \( x - 8 \). These remaining men completed the work in 18 days. Therefore, the total work done by these men is:
\[ \text{Total Work} = (x - 8) \times 18 \]

### Step 4: Set the Equations Equal
Since both expressions represent the same total work, we can set them equal to each other:
\[ x \times 10 = (x - 8) \times 18 \]

### Step 5: Expand the Equation
Expanding the right side gives us:
\[ 10x = 18x - 144 \]

### Step 6: Rearrange the Equation
Now, we will rearrange the equation to isolate \( x \):
\[ 10x - 18x = -144 \]
\[ -8x = -144 \]

### Step 7: Solve for \( x \)
Dividing both sides by -8 gives:
\[ x = \frac{144}{8} = 18 \]

### Conclusion
The original number of men is \( 18 \).