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 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 will use the relationship between the number of men, the number of days they work, and the total work done.

Let's denote:
- \( M \) = original number of men
- \( D_1 \) = original number of days to complete the job = 20 days
- \( D_2 \) = actual number of days taken to complete the job = 32 days
- \( W \) = total work (which remains constant)

### Step 1: Set up the equation for work done
The work done can be expressed in terms of men and days:
\[ M \times D_1 = W \]
This means:
\[ M \times 20 = W \]

### Step 2: Determine the number of men who actually worked
Since 12 men did not turn up, the number of men who actually worked is:
\[ M - 12 \]

### Step 3: Set up the equation for the actual work done
The actual work done by the remaining men can also be expressed as:
\[ (M - 12) \times D_2 = W \]
This means:
\[ (M - 12) \times 32 = W \]

### Step 4: Set the two equations for work equal to each other
Since both expressions equal the total work \( W \), we can set them equal:
\[ M \times 20 = (M - 12) \times 32 \]

### Step 5: Expand and simplify the equation
Expanding the right side:
\[ M \times 20 = M \times 32 - 12 \times 32 \]
This simplifies to:
\[ 20M = 32M - 384 \]

### Step 6: Rearrange the equation to isolate \( M \)
Now, we rearrange the equation:
\[ 32M - 20M = 384 \]
This simplifies to:
\[ 12M = 384 \]

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

### Conclusion
The original number of men in the group was **32**.

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