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 in 11 days less. How many persons were originally there ?

Options

A. 17
B. 24
C. 30
D. 22

Answer

To solve the problem step by step, let's denote the original number of persons as \( X \).

### Step 1: Set up the equations
We know that \( X \) persons can complete the work in 55 days. Therefore, the total work can be expressed in terms of person-days:
\[ \text{Total Work} = X \times 55 \]

If there are 6 more persons, the number of persons becomes \( X + 6 \), and they can complete the work in 44 days (since 11 days less than 55 days is 44 days). Thus, the total work can also be expressed as:
\[ \text{Total Work} = (X + 6) \times 44 \]

### Step 2: Set the two expressions for total work equal
Since both expressions represent the same total work, we can set them equal to each other:
\[ X \times 55 = (X + 6) \times 44 \]

### Step 3: Expand the equation
Now, we will expand the right side of the equation:
\[ 55X = 44X + 264 \]

### Step 4: Rearrange the equation
Next, we will rearrange the equation to isolate \( X \):
\[ 55X - 44X = 264 \]
\[ 11X = 264 \]

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

### Conclusion
Thus, the original number of persons is \( 24 \).