A certain number of persons can complete a piece of work in 55 days. If there were 6 persons more, the work could be finished 11 days Earlier. How many persons were there when the work started?

Options

A. 1. 17
B. 2. 24
C. 3. 30
D. 4. 22

Answer

To solve the problem step-by-step, let's denote the number of persons initially as \( x \).

### Step 1: Understand the work done
The problem states that a certain number of persons can complete the work in 55 days. This means that the total work can be expressed in terms of person-days. The total work \( W \) can be calculated as:
\[ W = x \times 55 \]

### Step 2: Work done with additional persons
If there were 6 more persons, the number of persons becomes \( x + 6 \). The work can then be completed in 11 days earlier, which means it can be completed in:
\[ 55 - 11 = 44 \text{ days} \]
Thus, the total work can also be expressed as:
\[ W = (x + 6) \times 44 \]

### Step 3: Set up the equation
Since both expressions represent the same total work \( W \), we can set them equal to each other:
\[ x \times 55 = (x + 6) \times 44 \]

### Step 4: Expand and simplify the equation
Expanding the right side of the equation gives:
\[ 55x = 44x + 264 \]
Now, we can isolate \( x \) by moving \( 44x \) to the left side:
\[ 55x - 44x = 264 \]
This simplifies to:
\[ 11x = 264 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 11 to find \( x \):
\[ x = \frac{264}{11} = 24 \]

### Conclusion
Thus, the number of persons when the work started was \( 24 \).