Two horses were sold at Rs 1599 each. First was sold at 25% profit and second at 20% loss. Find the over all profit or loss %.

Answer

To solve the problem step by step, we need to find the cost price of each horse based on the selling price and the profit/loss percentages given.

### Step-by-Step Solution:

1. **Identify the Selling Price (SP)**:
Both horses are sold for Rs 1599 each.
\[ SP_1 = SP_2 = 1599 \]

2. **Calculate the Cost Price (CP) of the First Horse**:
The first horse is sold at a 25% profit.
Let the cost price of the first horse be \( CP_1 \).
\[ SP_1 = CP_1 + 0.25 \times CP_1 = 1.25 \times CP_1 \]
Rearranging gives:
\[ CP_1 = \frac{SP_1}{1.25} = \frac{1599}{1.25} = 1279.20 \]

3. **Calculate the Cost Price (CP) of the Second Horse**:
The second horse is sold at a 20% loss.
Let the cost price of the second horse be \( CP_2 \).
\[ SP_2 = CP_2 - 0.20 \times CP_2 = 0.80 \times CP_2 \]
Rearranging gives:
\[ CP_2 = \frac{SP_2}{0.80} = \frac{1599}{0.80} = 1998.75 \]

4. **Calculate the Total Cost Price (TCP)**:
Now, we can find the total cost price of both horses:
\[ TCP = CP_1 + CP_2 = 1279.20 + 1998.75 = 3277.95 \]

5. **Calculate the Total Selling Price (TSP)**:
The total selling price of both horses is:
\[ TSP = SP_1 + SP_2 = 1599 + 1599 = 3198 \]

6. **Calculate the Overall Profit or Loss**:
To find the overall profit or loss, we subtract the total cost price from the total selling price:
\[ \text{Profit or Loss} = TSP - TCP = 3198 - 3277.95 = -79.95 \]
Since this value is negative, it indicates a loss.

7. **Calculate the Loss Percentage**:
The loss percentage can be calculated using the formula:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{TCP}\right) \times 100 \]
Substituting the values:
\[ \text{Loss Percentage} = \left(\frac{79.95}{3277.95}\right) \times 100 \approx 2.44\% \]

### Final Answer:
The overall loss percentage is approximately **2.44%**.