Two horses were sold at Rs 1710. First was sold at 10% loss and second at 25% profit. If the cost price of first horse is equal to selling price of second horse. Find the over all profit or loss in rupees.

Answer

To solve the problem step by step, we will first define the variables and then use the information given to find the cost prices and ultimately the overall profit or loss.

### Step 1: Define Variables
Let:
- Cost Price of the first horse = CP1
- Cost Price of the second horse = CP2

### Step 2: Selling Prices
From the problem, we know:
- The first horse is sold at a 10% loss.
- The second horse is sold at a 25% profit.

Thus, the selling prices can be calculated as follows:
- Selling Price of the first horse (SP1) = CP1 - 10% of CP1 = CP1 × (1 - 0.10) = 0.90 × CP1
- Selling Price of the second horse (SP2) = CP2 + 25% of CP2 = CP2 × (1 + 0.25) = 1.25 × CP2

### Step 3: Total Selling Price
According to the question, the total selling price of both horses is Rs 1710:
\[ SP1 + SP2 = 1710 \]
Substituting the expressions for SP1 and SP2:
\[ 0.90 \times CP1 + 1.25 \times CP2 = 1710 \]

### Step 4: Relationship Between Cost Prices
The problem states that the cost price of the first horse is equal to the selling price of the second horse:
\[ CP1 = SP2 \]
Substituting the expression for SP2:
\[ CP1 = 1.25 \times CP2 \]

### Step 5: Substitute CP1 in the Total Selling Price Equation
Now, we can substitute CP1 in the total selling price equation:
\[ 0.90 \times (1.25 \times CP2) + 1.25 \times CP2 = 1710 \]
This simplifies to:
\[ 1.125 \times CP2 + 1.25 \times CP2 = 1710 \]
Combining the terms:
\[ (1.125 + 1.25) \times CP2 = 1710 \]
\[ 2.375 \times CP2 = 1710 \]

### Step 6: Calculate CP2
Now, we can solve for CP2:
\[ CP2 = \frac{1710}{2.375} \]
Calculating this gives:
\[ CP2 = 720 \]

### Step 7: Calculate CP1
Using the relationship \( CP1 = 1.25 \times CP2 \):
\[ CP1 = 1.25 \times 720 = 900 \]

### Step 8: Calculate Total Cost Price
Now, we can find the total cost price:
\[ Total \, CP = CP1 + CP2 = 900 + 720 = 1620 \]

### Step 9: Calculate Overall Profit or Loss
Finally, we can calculate the overall profit or loss:
\[ Profit/Loss = Total \, SP - Total \, CP = 1710 - 1620 = 90 \]
Since the result is positive, it indicates a profit.

### Conclusion
The overall profit is Rs 90.

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