If 40 men can finish a piece of work in 60 days. In how many days will 75 , men finish the same work ?

Answer

To solve the problem, we can use the concept of work done, which is based on the number of men and the number of days they work. Here's the step-by-step solution:

### Step 1: Understand the Work Done
We know that 40 men can finish the work in 60 days. Therefore, the total work can be expressed in terms of man-days.

**Total Work = Number of Men × Number of Days**
Total Work = 40 men × 60 days = 2400 man-days

### Step 2: Set Up the Equation for 75 Men
Now, we need to find out how many days (let's call it 'D') it will take for 75 men to complete the same amount of work.

**Total Work = Number of Men × Number of Days**
2400 man-days = 75 men × D days

### Step 3: Solve for D
Now we can rearrange the equation to solve for D:

D = Total Work / Number of Men
D = 2400 man-days / 75 men

### Step 4: Perform the Calculation
Now we will perform the division:

D = 2400 / 75

To simplify this calculation:

1. Divide both the numerator and the denominator by 15:
- 2400 ÷ 15 = 160
- 75 ÷ 15 = 5

So now we have:

D = 160 / 5 = 32 days

### Conclusion
Therefore, 75 men will finish the same work in **32 days**.

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