9 व्यक्ति किसी काम को 5 दिन में करते हैं। यदि इस काम को 3 दिनों में खत्म करना है तब कितने व्यक्तियों की अतिरिक्त आवश्यकता होगी

Options

A. 5
B. 6
C. 8
D. 7

Answer

To solve the problem step by step, we first need to understand the relationship between the number of people, the number of days, and the amount of work done.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- 9 people can complete the work in 5 days.
- We need to find out how many additional people are required to complete the same work in 3 days.

2. **Calculate the Total Work in Person-Days:**
- Total work can be calculated as:
\[ \text{Total Work} = \text{Number of People} \times \text{Number of Days} \]
- For the given situation:
\[ \text{Total Work} = 9 \text{ people} \times 5 \text{ days} = 45 \text{ person-days} \]

3. **Determine the Number of People Required to Complete the Work in 3 Days:**
- Let \( x \) be the total number of people required to finish the work in 3 days.
- The equation for work done in 3 days will be:
\[ \text{Total Work} = x \text{ people} \times 3 \text{ days} \]
- Setting the total work equal to 45 person-days:
\[ x \times 3 = 45 \]

4. **Solve for \( x \):**
- Divide both sides by 3:
\[ x = \frac{45}{3} = 15 \]

5. **Calculate the Additional Number of People Required:**
- We already have 9 people, so the additional number of people needed is:
\[ \text{Additional People} = x - 9 = 15 - 9 = 6 \]

### Final Answer:
The additional number of people required to complete the work in 3 days is **6**.