Working 10 hours a day, Aman can complete a piece of work in 18 days. How many hours a day should he work so as to finish the work in 15 days ?

Options

A. 10
B. 12
C. 16
D. 18

Answer

To solve the problem step by step, we can use the relationship between work, efficiency, and time.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- Aman works 10 hours a day.
- He completes the work in 18 days.

2. **Calculate Total Work**:
- Total work can be calculated as:
\[ \text{Total Work} = \text{Hours per Day} \times \text{Days} = 10 \, \text{hours/day} \times 18 \, \text{days} = 180 \, \text{hours} \]

3. **Set Up the Equation for New Scenario**:
- We want to find out how many hours per day (let's call it \( x \)) Aman needs to work to finish the same work in 15 days.
- The equation for total work in this scenario will be:
\[ \text{Total Work} = x \, \text{hours/day} \times 15 \, \text{days} \]

4. **Equate the Total Work**:
- Since the total work remains the same, we can set the two equations equal to each other:
\[ 180 \, \text{hours} = x \, \text{hours/day} \times 15 \, \text{days} \]

5. **Solve for \( x \)**:
- Rearranging the equation gives:
\[ x = \frac{180 \, \text{hours}}{15 \, \text{days}} = 12 \, \text{hours/day} \]

6. **Conclusion**:
- Aman needs to work **12 hours a day** to finish the work in 15 days.