A group of workers can complete a job in 120 days. If there were 4 more such workers then the work could be finished in 12 days less what was the actual strength of workers?

Options

A. 30 workers
B. 40 workers
C. 42 workers
D. 36 workers

Answer

To solve the problem step by step, we will use the concept of work done by a group of workers over a period of time.

### Step 1: Define the variables
Let the actual strength of the workers be \( x \). This means there are \( x \) workers.

### Step 2: Determine the total work done
The group of workers can complete the job in 120 days. Therefore, the total work \( W \) can be expressed as:
\[ W = \text{Number of workers} \times \text{Number of days} = x \times 120 \]

### Step 3: Analyze the scenario with additional workers
If there were 4 more workers, the number of workers would be \( x + 4 \). The work could then be finished in 12 days less, which means it would take \( 120 - 12 = 108 \) days.

### Step 4: Express the total work with the additional workers
The total work done with the additional workers can also be expressed as:
\[ W = (x + 4) \times 108 \]

### Step 5: Set the two expressions for work equal to each other
Since the total work \( W \) is the same in both scenarios, we can set the equations equal to each other:
\[ x \times 120 = (x + 4) \times 108 \]

### Step 6: Expand and simplify the equation
Expanding the right side:
\[ 120x = 108x + 432 \]

### Step 7: Rearrange the equation to isolate \( x \)
Subtract \( 108x \) from both sides:
\[ 120x - 108x = 432 \]
\[ 12x = 432 \]

### Step 8: Solve for \( x \)
Now, divide both sides by 12:
\[ x = \frac{432}{12} = 36 \]

### Conclusion
The actual strength of the workers is \( x = 36 \).