Certain men can do a piece of work in 22 days. If the number of men decreses by 55, then they will take 11 days more to comlete the same work. Find the number of men present intially.

Options

A. 165
B. 155
C. 185
D. 175

Explanation

To solve the problem, we will follow these steps:

### Step 1: Define Variables
Let the number of men initially be \( X \).

### Step 2: Calculate Work Done by Initial Men
If \( X \) men can complete the work in 22 days, the total work can be expressed in terms of man-days:
\[ \text{Total Work} = X \times 22 \]

### Step 3: Calculate Work Done by Reduced Number of Men
When the number of men decreases by 55, the number of men becomes \( X - 55 \). According to the problem, these men take 11 days more, which means they complete the work in:
\[ 22 + 11 = 33 \text{ days} \]
The total work done by these men can also be expressed as:
\[ \text{Total Work} = (X - 55) \times 33 \]

### Step 4: Set Up the Equation
Since both expressions represent the same total work, we can set them equal to each other:
\[ X \times 22 = (X - 55) \times 33 \]

### Step 5: Expand and Rearrange the Equation
Expanding the right side:
\[ 22X = 33X - 55 \times 33 \]
\[ 22X = 33X - 1815 \]
Now, rearranging the equation to isolate \( X \):
\[ 22X - 33X = -1815 \]
\[ -11X = -1815 \]
Dividing both sides by -11:
\[ X = \frac{1815}{11} \]
\[ X = 165 \]

### Step 6: Conclusion
Thus, the number of men present initially is \( 165 \).