A certain job was assigned to a group of men to do in 20 days. But 12 men did not turn up for the job and the remaining men did the job in 32 days. The original number of men in the group was :

Options

A. 32
B. 36
C. 42
D. 40

Answer

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

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

### Step 2: Calculate the Total Work
The total work can be expressed in terms of man-days. If \( x \) men can complete the job in 20 days, the total work \( W \) is:
\[ W = x \times 20 \]

### Step 3: Account for the Men Who Did Not Turn Up
Since 12 men did not turn up, the number of men who actually worked is:
\[ x - 12 \]

### Step 4: Calculate the Work Done by Remaining Men
The remaining men completed the job in 32 days. Therefore, the work done can also be expressed as:
\[ W = (x - 12) \times 32 \]

### Step 5: Set the Two Expressions for Work Equal
Since both expressions represent the same total work, we can set them equal to each other:
\[ x \times 20 = (x - 12) \times 32 \]

### Step 6: Expand and Rearrange the Equation
Expanding the right side gives:
\[ 20x = 32x - 384 \]
Now, rearranging the equation to isolate \( x \):
\[ 20x - 32x = -384 \]
\[ -12x = -384 \]

### Step 7: Solve for \( x \)
Dividing both sides by -12 gives:
\[ x = \frac{384}{12} = 32 \]

### Conclusion
The original number of men in the group was \( \boxed{32} \).

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