A man sells two horses for Rs 1710. The cost price of first horses is equal to the selling price of 2nd horse. If the loss on first horse is 10% and he earns 25% profit on second horses. Find the total loss or profit.

Options

A. Rs 90
B. Rs 120
C. Rs 80
D. Rs 110

Answer

To solve the problem step by step, we will analyze the selling and cost prices of the two horses based on the given information.

### Step 1: Define Variables
Let:
- Cost Price of the first horse = CP1
- Selling Price of the first horse = SP1
- Cost Price of the second horse = CP2
- Selling Price of the second horse = SP2

### Step 2: Understand the Loss and Profit
- The loss on the first horse is 10%. Therefore, we can express the selling price of the first horse as:
\[ SP1 = CP1 - (10\% \text{ of } CP1) = CP1 \times (1 - 0.10) = 0.90 \times CP1 \]

- The profit on the second horse is 25%. Therefore, we can express the selling price of the second horse as:
\[ SP2 = CP2 + (25\% \text{ of } CP2) = CP2 \times (1 + 0.25) = 1.25 \times CP2 \]

### Step 3: Relate Cost Price of First Horse to Selling Price of Second Horse
According to the problem, 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 4: Total Selling Price
The total selling price of the two horses is given as Rs 1710:
\[ SP1 + SP2 = 1710 \]
Substituting the expressions for SP1 and SP2:
\[ 0.90 \times CP1 + 1.25 \times CP2 = 1710 \]

### Step 5: Substitute CP1 in Terms of CP2
From the earlier relation \( CP1 = 1.25 \times CP2 \), substitute this into the total selling price equation:
\[ 0.90 \times (1.25 \times CP2) + 1.25 \times CP2 = 1710 \]
\[ 1.125 \times CP2 + 1.25 \times CP2 = 1710 \]
Combining the terms:
\[ 2.375 \times CP2 = 1710 \]

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

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

### Step 8: Calculate Selling Prices
Now we can find the selling prices:
- For the first horse:
\[ SP1 = 0.90 \times CP1 = 0.90 \times 900 = 810 \]
- For the second horse:
\[ SP2 = 1.25 \times CP2 = 1.25 \times 720 = 900 \]

### Step 9: Calculate Total Cost Price
Now we can find the total cost price:
\[ \text{Total Cost Price} = CP1 + CP2 = 900 + 720 = 1620 \]

### Step 10: Calculate Total Profit or Loss
Now, we can find the total profit or loss:
\[ \text{Total Selling Price} = SP1 + SP2 = 810 + 900 = 1710 \]
\[ \text{Profit} = \text{Total Selling Price} - \text{Total Cost Price} = 1710 - 1620 = 90 \]

### Conclusion
The man made a profit of Rs 90.