40 persons consume 200kg of rice is 30 days, In how many days will 30 persons consume 500kg of rice?

Options

A. 90
B. 120
C. 80
D. 100

Answer

To solve the problem step by step, we can use the concept of work done, which relates the number of persons, the amount of rice consumed, and the number of days taken.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- 40 persons consume 200 kg of rice in 30 days.
- We need to find out how many days 30 persons will take to consume 500 kg of rice.

2. **Set Up the Work Done Formula:**
- We can use the formula:
\[ \frac{M_1 \times D_1}{W_1} = \frac{M_2 \times D_2}{W_2} \]
Where:
- \( M_1 = 40 \) (persons)
- \( D_1 = 30 \) (days)
- \( W_1 = 200 \) (kg of rice)
- \( M_2 = 30 \) (persons)
- \( D_2 = ? \) (days, which we need to find)
- \( W_2 = 500 \) (kg of rice)

3. **Substituting the Values into the Formula:**
\[ \frac{40 \times 30}{200} = \frac{30 \times D_2}{500} \]

4. **Simplifying the Left Side:**
- Calculate \( \frac{40 \times 30}{200} \):
\[ \frac{1200}{200} = 6 \]

5. **Setting Up the Equation:**
- Now we have:
\[ 6 = \frac{30 \times D_2}{500} \]

6. **Cross-Multiplying to Solve for \( D_2 \):**
\[ 6 \times 500 = 30 \times D_2 \]
\[ 3000 = 30 \times D_2 \]

7. **Dividing Both Sides by 30:**
\[ D_2 = \frac{3000}{30} = 100 \]

8. **Conclusion:**
- Therefore, 30 persons will consume 500 kg of rice in **100 days**.