A fodder stock lasts for 36 days for 20 cows. How long will it last for 15 cows ?

Options

A. 54 days
B. 42 days
C. 56 days
D. None of these

Answer

To solve the problem, we need to determine how long the fodder stock will last for 15 cows, given that it lasts for 36 days for 20 cows. We can use the concept of "cow-days" to find the solution.

### Step-by-Step Solution:

1. **Calculate Total Cow-Days**:
The total amount of fodder can be expressed in terms of cow-days. Since 20 cows can eat the fodder for 36 days, the total cow-days of fodder is:
\[ \text{Total Cow-Days} = \text{Number of Cows} \times \text{Number of Days} = 20 \text{ cows} \times 36 \text{ days} = 720 \text{ cow-days} \]

2. **Determine Cow-Days for 15 Cows**:
Now, we need to find out how many days the same amount of fodder (720 cow-days) will last for 15 cows. Let \( D \) be the number of days the fodder will last for 15 cows. The equation will be:
\[ \text{Total Cow-Days} = \text{Number of Cows} \times \text{Number of Days} \]
Substituting the values we have:
\[ 720 \text{ cow-days} = 15 \text{ cows} \times D \text{ days} \]

3. **Solve for D**:
Now, we will solve for \( D \):
\[ D = \frac{720 \text{ cow-days}}{15 \text{ cows}} = 48 \text{ days} \]

4. **Conclusion**:
Therefore, the fodder will last for 48 days for 15 cows.

### Final Answer:
The fodder stock will last for **48 days** for 15 cows.

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