A certain number of men can do a work in 35 days. If there were 10 men more it could be finished in 10 days less. How many men are there?

Options

A. 20
B. 25
C. 30
D. 32

Answer

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

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

### Step 2: Set Up the Work Equation
According to the problem, \( X \) men can complete the work in 35 days. The total work done can be expressed as:
\[ \text{Total Work} = X \times 35 \]

### Step 3: Set Up the New Work Equation
If there are 10 more men, the number of men becomes \( X + 10 \), and they can complete the work in 25 days (10 days less than 35 days). The total work done in this case can be expressed as:
\[ \text{Total Work} = (X + 10) \times 25 \]

### Step 4: Set the Two Equations Equal
Since the total work remains the same in both scenarios, we can set the two equations equal to each other:
\[ X \times 35 = (X + 10) \times 25 \]

### Step 5: Expand and Simplify the Equation
Expanding the right side gives:
\[ 35X = 25X + 250 \]

### Step 6: Rearrange the Equation
Now, we can rearrange the equation to isolate \( X \):
\[ 35X - 25X = 250 \]
\[ 10X = 250 \]

### Step 7: Solve for \( X \)
Dividing both sides by 10 gives:
\[ X = 25 \]

### Conclusion
The number of men is \( 25 \).

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