A person bought a horse and a vehicle for Rs 40,000 he sold horse at 10% profit and vhicle at 5% loss on whole transection he got profit of 1% . Find C.P. of horse?

Answer

To find the cost price (C.P.) of the horse, we will follow these steps:

### Step 1: Understand the given information
- Total cost price of the horse and vehicle = Rs 40,000
- Profit on horse = 10%
- Loss on vehicle = 5%
- Overall profit on the transaction = 1%

### Step 2: Set up the equations
Let the cost price of the horse be \( x \) and the cost price of the vehicle be \( 40,000 - x \).

### Step 3: Calculate the selling prices
1. Selling price of the horse:
\[ \text{Selling Price of Horse} = x + 10\% \text{ of } x = x + 0.1x = 1.1x \]

2. Selling price of the vehicle:
\[ \text{Selling Price of Vehicle} = (40,000 - x) - 5\% \text{ of } (40,000 - x) = (40,000 - x) - 0.05(40,000 - x) \]
\[ = (40,000 - x) \times (1 - 0.05) = (40,000 - x) \times 0.95 = 0.95(40,000 - x) \]

### Step 4: Calculate the total selling price
Total selling price = Selling price of horse + Selling price of vehicle
\[ \text{Total Selling Price} = 1.1x + 0.95(40,000 - x) \]

### Step 5: Set up the equation for overall profit
Since the overall profit is 1%, the total selling price can also be expressed as:
\[ \text{Total Selling Price} = \text{Total Cost Price} + 1\% \text{ of Total Cost Price} \]
\[ = 40,000 + 0.01 \times 40,000 = 40,000 + 400 = 40,400 \]

### Step 6: Equate the two expressions for total selling price
\[ 1.1x + 0.95(40,000 - x) = 40,400 \]

### Step 7: Simplify the equation
Expanding the equation:
\[ 1.1x + 0.95 \times 40,000 - 0.95x = 40,400 \]
\[ 1.1x - 0.95x + 38,000 = 40,400 \]
\[ 0.15x + 38,000 = 40,400 \]

### Step 8: Solve for \( x \)
Subtract 38,000 from both sides:
\[ 0.15x = 40,400 - 38,000 \]
\[ 0.15x = 2,400 \]
Now, divide by 0.15:
\[ x = \frac{2,400}{0.15} = 16,000 \]

### Conclusion
The cost price of the horse is Rs 16,000.

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