Some staff promised to do a job in 18 days, but 6 of them went on leave. So the remaining men took 20 days to complete the job. How many men were there originally?

Options

A. 55
B. 62
C. 56
D. 60

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define the variables
Let \( X \) be the original number of staff members.

### Step 2: Set up the equations
The staff promised to complete the job in 18 days. Therefore, the total work done can be expressed as:
\[ \text{Work} = \text{Number of persons} \times \text{Number of days} = X \times 18 \]

When 6 staff members went on leave, the remaining staff is \( X - 6 \). They completed the same job in 20 days:
\[ \text{Work} = (X - 6) \times 20 \]

### Step 3: Equate the two expressions for work
Since the total work done is the same in both cases, we can set the two equations equal to each other:
\[ X \times 18 = (X - 6) \times 20 \]

### Step 4: Expand and simplify the equation
Expanding the right side:
\[ 18X = 20X - 120 \]

### Step 5: Rearrange the equation
Now, move all terms involving \( X \) to one side:
\[ 18X - 20X = -120 \]
\[ -2X = -120 \]

### Step 6: Solve for \( X \)
Dividing both sides by -2:
\[ X = \frac{120}{2} = 60 \]

### Conclusion
Thus, the original number of staff members was \( 60 \).

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