If a man earns ₹ 2,000 for his first 50 hours of work in a week and then he is paid one and one half times his regular hourly rate for any additional hours, then how many extra hours must he work to make ₹ 2,300 in a week is:

Options

A. 4 hours
B. 5 hours
C. 6 hours
D. 7 hours

Answer

To solve the problem, we need to determine how many extra hours a man must work to earn a total of ₹2,300 in a week, given that he earns ₹2,000 for the first 50 hours of work.

### Step-by-Step Solution:

1. **Calculate the Regular Hourly Rate:**
- The man earns ₹2,000 for the first 50 hours of work.
- To find the hourly rate, we divide the total earnings by the number of hours worked.
\[ \text{Regular Hourly Rate} = \frac{2000}{50} = 40 \text{ rupees/hour} \]

**Hint:** To find the hourly rate, divide total earnings by total hours worked.

2. **Determine the Extra Hourly Rate:**
- For any additional hours worked beyond the first 50 hours, he is paid one and one half times his regular hourly rate.
\[ \text{Extra Hourly Rate} = 1.5 \times 40 = 60 \text{ rupees/hour} \]

**Hint:** Multiply the regular hourly rate by 1.5 to find the extra hourly rate.

3. **Calculate the Additional Earnings Needed:**
- The man wants to earn a total of ₹2,300. He has already earned ₹2,000 from the first 50 hours.
- We need to find out how much more he needs to earn.
\[ \text{Additional Earnings Needed} = 2300 - 2000 = 300 \text{ rupees} \]

**Hint:** Subtract the amount already earned from the total desired earnings to find the additional amount needed.

4. **Determine the Number of Extra Hours Required:**
- To find out how many extra hours he needs to work to earn the additional ₹300 at the extra hourly rate:
\[ \text{Extra Hours} = \frac{\text{Additional Earnings Needed}}{\text{Extra Hourly Rate}} = \frac{300}{60} = 5 \text{ hours} \]

**Hint:** Divide the additional earnings needed by the extra hourly rate to find the number of extra hours required.

### Final Answer:
The man must work **5 extra hours** to make ₹2,300 in a week.