A horse and a carriage together cost 8000. If by selling the horse at a profit of 10% and the carriage at a loss of 10%, a total profit of 2.5% is made, then what is the cost price of the horse?

Options

A. 3000
B. 6000
C. 2000
D. 5000

Answer

To find the cost price of the horse, we can break down the problem step by step.

### Step 1: Define Variables
Let the cost price of the horse be \( X \) and the cost price of the carriage be \( 8000 - X \).

### Step 2: Calculate Selling Prices
- Selling price of the horse (with a profit of 10%):
\[ SP_{\text{horse}} = X + 0.1X = 1.1X \]

- Selling price of the carriage (with a loss of 10%):
\[ SP_{\text{carriage}} = (8000 - X) - 0.1(8000 - X) = (8000 - X) \times 0.9 = 0.9(8000 - X) \]

### Step 3: Total Selling Price
The total selling price when both are sold is:
\[ SP_{\text{total}} = SP_{\text{horse}} + SP_{\text{carriage}} = 1.1X + 0.9(8000 - X) \]

### Step 4: Simplify Total Selling Price
Substituting the expression for the selling price of the carriage:
\[ SP_{\text{total}} = 1.1X + 0.9(8000) - 0.9X \]
\[ = 1.1X - 0.9X + 7200 = 0.2X + 7200 \]

### Step 5: Calculate Total Profit
The total cost price is \( 8000 \). Given that the total profit is 2.5%, the total selling price can also be expressed as:
\[ SP_{\text{total}} = CP + \text{Profit} = 8000 + 0.025 \times 8000 = 8000 + 200 = 8200 \]

### Step 6: Set Up the Equation
Now we can set the two expressions for total selling price equal to each other:
\[ 0.2X + 7200 = 8200 \]

### Step 7: Solve for \( X \)
Subtract 7200 from both sides:
\[ 0.2X = 8200 - 7200 \]
\[ 0.2X = 1000 \]

Now, divide by 0.2:
\[ X = \frac{1000}{0.2} = 5000 \]

### Conclusion
The cost price of the horse is \( \text{Rs. } 5000 \).

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