'x' number of men can finish a piece of work in 30 days. If there were 6 men more, the work could be finished in 10 days less. The original number of men is

Options

A. 6
B. 10
C. 12
D. 15

Answer

To solve the problem step by step, let's define the variables and set up the equations based on the information provided.

### Step 1: Define the variables
Let \( x \) be the original number of men. According to the problem, these \( x \) men can complete the work in 30 days.

### Step 2: Calculate the total work
The total work can be expressed in terms of man-days. Since \( x \) men complete the work in 30 days, the total work \( W \) is:
\[ W = x \times 30 \]

### Step 3: Set up the equation for the new scenario
If there are 6 more men, the total number of men becomes \( x + 6 \). The work can now be completed in 20 days (30 days - 10 days). Therefore, the total work can also be expressed as:
\[ W = (x + 6) \times 20 \]

### Step 4: Set the two expressions for work equal to each other
Since both expressions represent the same total work \( W \), we can set them equal:
\[ x \times 30 = (x + 6) \times 20 \]

### Step 5: Expand and simplify the equation
Expanding the right side:
\[ 30x = 20x + 120 \]

### Step 6: Rearranging the equation
Now, we can rearrange the equation to isolate \( x \):
\[ 30x - 20x = 120 \]
\[ 10x = 120 \]

### Step 7: Solve for \( x \)
Dividing both sides by 10 gives:
\[ x = 12 \]

### Conclusion
The original number of men is \( \boxed{12} \).

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