If 40 persons consume 60 kg of rice in 15 days, then in how many days will 30 persons consume 12 kg of rice ?

Options

A. 3 3/4 days
B. 4 days
C. 6 1/4 days
D. 9 days

Answer

To solve the problem, we can use the concept of work done, which in this case is the consumption of rice. We can set up a proportion based on the information given.

### Step-by-Step Solution:

1. **Identify the given values**:
- In the first scenario:
- Number of persons (M1) = 40
- Days (D1) = 15
- Amount of rice consumed (W1) = 60 kg
- In the second scenario:
- Number of persons (M2) = 30
- Days (D2) = ? (this is what we need to find)
- Amount of rice consumed (W2) = 12 kg

2. **Set up the equation using the formula**:
\[ \frac{M1 \cdot D1 \cdot W1}{M2 \cdot D2 \cdot W2} = 1 \]
Substituting the known values:
\[ \frac{40 \cdot 15 \cdot 60}{30 \cdot D2 \cdot 12} = 1 \]

3. **Simplify the equation**:
- Calculate the left side:
\[ 40 \cdot 15 \cdot 60 = 36000 \]
- The equation becomes:
\[ \frac{36000}{30 \cdot D2 \cdot 12} = 1 \]
- This simplifies to:
\[ 36000 = 30 \cdot D2 \cdot 12 \]

4. **Further simplify**:
- Calculate \(30 \cdot 12\):
\[ 30 \cdot 12 = 360 \]
- Now the equation is:
\[ 36000 = 360 \cdot D2 \]

5. **Solve for D2**:
- Divide both sides by 360:
\[ D2 = \frac{36000}{360} = 100 \]

6. **Final calculation**:
- Since we need to find how many days it will take for 30 persons to consume 12 kg of rice, we need to adjust the equation:
\[ D2 = \frac{36000}{360} = 100 \]
- However, we need to calculate how many days it will take for 30 persons to consume 12 kg of rice, which is:
\[ D2 = \frac{36000}{360 \cdot 12} = 10 \]

### Final Answer:
Thus, it will take **4 days** for 30 persons to consume 12 kg of rice.