If 27 kg of carn would feed 42 horses for 21 days, in how many days would 36 kg of it feed 21 horses ?

Options

A. 28 days
B. 42 days
C. 56 days
D. 31 1/2 days

Answer

To solve the problem, we need to determine how many days 36 kg of corn can feed 21 horses, given that 27 kg of corn can feed 42 horses for 21 days. We will use the concept of work done, which can be expressed as:

\[ \text{Work} = \text{Number of Horses} \times \text{Days} \times \text{Amount of Corn} \]

### Step-by-Step Solution:

1. **Calculate the total amount of corn consumed by the first scenario:**
- We know that 27 kg of corn feeds 42 horses for 21 days.
- The total work done in the first scenario (W1) can be calculated as:
\[ W_1 = \text{Number of Horses} \times \text{Days} = 42 \text{ horses} \times 21 \text{ days} = 882 \text{ horse-days} \]

2. **Calculate the total amount of corn consumed per horse per day in the first scenario:**
- The amount of corn consumed per horse per day can be calculated as:
\[ \text{Corn per horse per day} = \frac{27 \text{ kg}}{42 \text{ horses} \times 21 \text{ days}} = \frac{27}{882} \text{ kg} \]

3. **Set up the equation for the second scenario:**
- In the second scenario, we need to find out how many days (let's call it \(d_2\)) 36 kg of corn can feed 21 horses.
- The total work done in the second scenario (W2) is:
\[ W_2 = 21 \text{ horses} \times d_2 \text{ days} \]

4. **Set the work done equal to the amount of corn available:**
- We can express the total work done in terms of the amount of corn:
\[ W_2 = \frac{36 \text{ kg}}{\text{Corn per horse per day}} = \frac{36 \text{ kg}}{\frac{27}{882}} = 36 \times \frac{882}{27} \]

5. **Calculate the total work done in the second scenario:**
- Now we can equate the two scenarios:
\[ 21 \times d_2 = 36 \times \frac{882}{27} \]

6. **Solve for \(d_2\):**
- First, calculate \(36 \times \frac{882}{27}\):
\[ 36 \times \frac{882}{27} = 36 \times 32.6667 \approx 1186.67 \]
- Now, divide by 21 to find \(d_2\):
\[ d_2 = \frac{1186.67}{21} \approx 56.0 \text{ days} \]

### Final Answer:
Thus, 36 kg of corn would feed 21 horses for approximately **56 days**.