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 can follow these instructions:

### Step 1: Define the variables
Let the total number of workers be \( x \).

### Step 2: Calculate the total work done
If \( x \) workers can complete the job in 120 days, the total work can be expressed as:
\[ \text{Total Work} = \text{Number of Workers} \times \text{Number of Days} = 120x \]

### Step 3: Work done with additional workers
If there are 4 more workers, then the total number of workers becomes \( x + 4 \). The work can be completed in 12 days less, which means it will take \( 120 - 12 = 108 \) days. Therefore, the total work can also be expressed as:
\[ \text{Total Work} = (x + 4) \times 108 \]

### Step 4: Set the equations equal
Since both expressions represent the same total work, we can set them equal to each other:
\[ 120x = (x + 4) \times 108 \]

### Step 5: Expand and simplify the equation
Expanding the right side gives:
\[ 120x = 108x + 432 \]

### Step 6: Rearrange the equation
Now, we can rearrange the equation to isolate \( x \):
\[ 120x - 108x = 432 \]
\[ 12x = 432 \]

### Step 7: Solve for \( x \)
Dividing both sides by 12 gives:
\[ x = \frac{432}{12} = 36 \]

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