Working 5 hours a day, Shivam can read a book in 24 days. How many hours a day should he work so as to finish the same work in 8 days?

Options

A. 12
B. 18
C. 15
D. 21

Answer

To solve the problem, we need to determine how many hours a day Shivam should work to finish reading the book in 8 days, given that he can read it in 24 days by working 5 hours a day.

### Step-by-Step Solution:

1. **Calculate Total Work in Hours**:
- Shivam works 5 hours a day for 24 days.
- Total work = Hours per day × Number of days = 5 hours/day × 24 days = 120 hours.

2. **Determine Daily Work Requirement for 8 Days**:
- If Shivam wants to finish the same work in 8 days, we need to find out how many hours he needs to work each day.
- Let \( x \) be the number of hours he needs to work each day.
- Total work = Daily work × Number of days = \( x \) hours/day × 8 days.

3. **Set Up the Equation**:
- We know the total work is the same, so we can set up the equation:
\[ x \times 8 = 120 \]

4. **Solve for \( x \)**:
- To find \( x \), divide both sides of the equation by 8:
\[ x = \frac{120}{8} = 15 \]

5. **Conclusion**:
- Shivam needs to work 15 hours a day to finish reading the book in 8 days.

### Final Answer:
Shivam should work **15 hours a day**.