If 8 men can do a piece of work in 15 days, how many men are required to do the same piece of work in 10 days ?

Answer

To solve the problem, we can use the relationship between the number of men, the number of days, and the work done. The formula we will use is:

\[ n_1 \times d_1 = n_2 \times d_2 \]

Where:
- \( n_1 \) = number of men initially (8 men)
- \( d_1 \) = number of days initially (15 days)
- \( n_2 \) = number of men required (unknown)
- \( d_2 \) = number of days required (10 days)

### Step-by-Step Solution:

1. **Identify the given values:**
- \( n_1 = 8 \) (the number of men)
- \( d_1 = 15 \) (the number of days)
- \( d_2 = 10 \) (the number of days for which we want to find the number of men)
- \( n_2 = ? \) (the number of men required)

2. **Set up the equation using the formula:**
\[ n_1 \times d_1 = n_2 \times d_2 \]
Substituting the known values:
\[ 8 \times 15 = n_2 \times 10 \]

3. **Calculate the left side of the equation:**
\[ 8 \times 15 = 120 \]
So, we have:
\[ 120 = n_2 \times 10 \]

4. **Rearrange the equation to solve for \( n_2 \):**
\[ n_2 = \frac{120}{10} \]

5. **Calculate \( n_2 \):**
\[ n_2 = 12 \]

### Conclusion:
The number of men required to do the same piece of work in 10 days is **12 men**.

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