Two horses were sold at Rs 12600. First horse was sold at 20% loss and second at 25% profit. If the cost price of first horse is equal to selling price of second horse. Find the overall profit/loss.

Options

A. Rs 360
B. Rs 440
C. No profit or no loss
D. Rs 542

Answer

To solve the problem step by step, let's denote the cost price (CP) and selling price (SP) of the two horses.

### Step 1: Define Variables
Let:
- CP of the first horse = \( CP_1 \)
- CP of the second horse = \( CP_2 \)
- SP of the first horse = \( SP_1 \)
- SP of the second horse = \( SP_2 \)

### Step 2: Set Up the Equations
According to the problem:
1. The first horse is sold at a 20% loss, so:
\[ SP_1 = CP_1 - 0.20 \times CP_1 = 0.80 \times CP_1 \]

2. The second horse is sold at a 25% profit, so:
\[ SP_2 = CP_2 + 0.25 \times CP_2 = 1.25 \times CP_2 \]

3. The total selling price of both horses is given as Rs 12,600:
\[ SP_1 + SP_2 = 12600 \]

4. It is also given that the cost price of the first horse is equal to the selling price of the second horse:
\[ CP_1 = SP_2 \]

### Step 3: Substitute and Solve
From the equations above, we can substitute \( SP_2 \) in terms of \( CP_2 \):
\[ CP_1 = 1.25 \times CP_2 \]

Now substituting \( SP_1 \) and \( SP_2 \) into the total selling price equation:
\[ 0.80 \times CP_1 + 1.25 \times CP_2 = 12600 \]

Substituting \( CP_1 \) from the previous equation:
\[ 0.80 \times (1.25 \times CP_2) + 1.25 \times CP_2 = 12600 \]
\[ 1.00 \times CP_2 + 1.25 \times CP_2 = 12600 \]
\[ 2.25 \times CP_2 = 12600 \]

### Step 4: Calculate \( CP_2 \)
Now, solving for \( CP_2 \):
\[ CP_2 = \frac{12600}{2.25} = 5600 \]

### Step 5: Find \( CP_1 \)
Using \( CP_1 = 1.25 \times CP_2 \):
\[ CP_1 = 1.25 \times 5600 = 7000 \]

### Step 6: Calculate Selling Prices
Now, calculate the selling prices:
1. For the first horse:
\[ SP_1 = 0.80 \times CP_1 = 0.80 \times 7000 = 5600 \]

2. For the second horse:
\[ SP_2 = 1.25 \times CP_2 = 1.25 \times 5600 = 7000 \]

### Step 7: Calculate Total Cost Price and Selling Price
Total cost price:
\[ CP_{total} = CP_1 + CP_2 = 7000 + 5600 = 12600 \]

Total selling price:
\[ SP_{total} = SP_1 + SP_2 = 5600 + 7000 = 12600 \]

### Step 8: Determine Profit or Loss
Now, we can determine the overall profit or loss:
\[ \text{Profit/Loss} = SP_{total} - CP_{total} = 12600 - 12600 = 0 \]

### Conclusion
Thus, there is no profit or loss.