A group of workers could complete a piece of work in 84 days. If there were 6 more workers, it would have taken 12 days less to finish the same piece of work. What was the actual strength of workers ?

Options

A. 42
B. 36
C. 48
D. 32

Answer

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

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

### Step 2: Calculate the Total Work
The total work done can be expressed in terms of the number of workers and the number of days they work. If \( x \) workers can complete the work in 84 days, then the total work \( W \) can be expressed as:
\[ W = x \times 84 \]

### Step 3: Set Up the Equation for Increased Workers
If there are 6 more workers, the total number of workers becomes \( x + 6 \). According to the problem, with these additional workers, the work can be completed in 12 days less, which means it would take 72 days (since \( 84 - 12 = 72 \)). The total work can also be expressed as:
\[ W = (x + 6) \times 72 \]

### Step 4: Equate the Two Expressions for Work
Since both expressions represent the same total work, we can set them equal to each other:
\[ x \times 84 = (x + 6) \times 72 \]

### Step 5: Expand and Simplify the Equation
Expanding the right side:
\[ 84x = 72x + 432 \]

### Step 6: Rearrange the Equation
Now, we can rearrange the equation to isolate \( x \):
\[ 84x - 72x = 432 \]
\[ 12x = 432 \]

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

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