A work could be completed in 100 days by some workers. However, due to the absence of 10 workers, it was completed in 110 days. The original number of workers was:

Options

A. 100
B. 110
C. 55
D. 50

Answer

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

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

### Step 2: Set up the equation for the work done
If \( X \) workers can complete the work in 100 days, then the total work can be expressed in terms of worker-days:
\[ \text{Total Work} = X \times 100 \]

### Step 3: Set up the equation for the work done with fewer workers
If 10 workers are absent, then the number of workers becomes \( X - 10 \). These workers complete the same amount of work in 110 days:
\[ \text{Total Work} = (X - 10) \times 110 \]

### Step 4: Set the two expressions for total work equal to each other
Since both expressions represent the same total work, we can set them equal:
\[ X \times 100 = (X - 10) \times 110 \]

### Step 5: Expand and simplify the equation
Expanding the right side:
\[ 100X = 110X - 1100 \]

### Step 6: Rearrange the equation to isolate \( X \)
Now, let's move all terms involving \( X \) to one side and the constant to the other side:
\[ 100X - 110X = -1100 \]
\[ -10X = -1100 \]

### Step 7: Solve for \( X \)
Dividing both sides by -10 gives:
\[ X = \frac{1100}{10} = 110 \]

### Conclusion
The original number of workers was \( 110 \).

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