Some carpenters promised to do a job in 9 days but 5 of them were absent and remaining men did the job in 12 days. The original number of carpenters was

Options

A. 24
B. 20
C. 16
D. 18

Answer

To solve the problem step by step, we can follow this approach:

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

### Step 2: Calculate Total Work
The carpenters promised to complete the job in 9 days. Therefore, the total work can be expressed as:
\[ \text{Total Work} = \text{Number of Carpenters} \times \text{Days} = x \times 9 = 9x \]

### Step 3: Calculate Work Done by Remaining Carpenters
Since 5 carpenters were absent, the number of carpenters who actually worked is:
\[ x - 5 \]
They completed the job in 12 days, so the total work done can also be expressed as:
\[ \text{Total Work} = \text{Number of Remaining Carpenters} \times \text{Days} = (x - 5) \times 12 \]

### Step 4: Set Up the Equation
Since both expressions represent the total work, we can set them equal to each other:
\[ 9x = 12(x - 5) \]

### Step 5: Expand and Simplify the Equation
Expanding the right side:
\[ 9x = 12x - 60 \]
Now, rearranging the equation to isolate \( x \):
\[ 9x - 12x = -60 \]
\[ -3x = -60 \]

### Step 6: Solve for \( x \)
Dividing both sides by -3:
\[ x = 20 \]

### Conclusion
The original number of carpenters was \( 20 \).

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