A man purchases 5 horses and 10 cows for Rs 10000. He sells the horses at 15% profit and the cows at 10% loss. Thus he gets Rs 375 as profit Find the cost of 1 horse and 1 cow separately.

Answer

To solve the problem, we need to find the cost of one horse and one cow separately based on the given information. Let's break this down step by step.

### Step 1: Set up the equations
Let the cost of one horse be \( H \) and the cost of one cow be \( C \).

From the problem, we know:
- The total cost of 5 horses and 10 cows is Rs. 10,000.

This gives us our first equation:
\[ 5H + 10C = 10000 \quad \text{(1)} \]

### Step 2: Calculate the selling prices
Next, we calculate the selling prices based on the profit and loss percentages given.

- Selling price of horses:
- Profit on horses = 15%
- Selling price of one horse = \( H + 0.15H = 1.15H \)
- Total selling price for 5 horses = \( 5 \times 1.15H = 5.75H \)

- Selling price of cows:
- Loss on cows = 10%
- Selling price of one cow = \( C - 0.10C = 0.90C \)
- Total selling price for 10 cows = \( 10 \times 0.90C = 9C \)

### Step 3: Set up the profit equation
The total selling price of horses and cows combined gives us the total revenue. The profit made is Rs. 375.

Thus, we can set up our second equation:
\[ (5.75H + 9C) - 10000 = 375 \]
This simplifies to:
\[ 5.75H + 9C = 10375 \quad \text{(2)} \]

### Step 4: Solve the system of equations
Now we have a system of two equations:
1. \( 5H + 10C = 10000 \) (1)
2. \( 5.75H + 9C = 10375 \) (2)

We can solve these equations simultaneously.

From equation (1), we can express \( C \) in terms of \( H \):
\[ 10C = 10000 - 5H \implies C = \frac{10000 - 5H}{10} = 1000 - 0.5H \quad \text{(3)} \]

Now, substitute equation (3) into equation (2):
\[ 5.75H + 9(1000 - 0.5H) = 10375 \]
Expanding this gives:
\[ 5.75H + 9000 - 4.5H = 10375 \]
Combining like terms:
\[ (5.75H - 4.5H) + 9000 = 10375 \]
\[ 1.25H + 9000 = 10375 \]
Subtracting 9000 from both sides:
\[ 1.25H = 1375 \]
Dividing by 1.25:
\[ H = \frac{1375}{1.25} = 1100 \]

### Step 5: Find the cost of one cow
Now that we have \( H \), we can substitute back to find \( C \):
Using equation (3):
\[ C = 1000 - 0.5(1100) = 1000 - 550 = 450 \]

### Final Answer
- Cost of one horse \( H = 1100 \)
- Cost of one cow \( C = 450 \)