Two horses were sold at Rs 2380 each. First was sold at 20% profit and second at 25% loss. Find the over all profit or loss %

Answer

To find the overall profit or loss percentage when two horses are sold at the same selling price but with different profit and loss percentages, we can follow these steps:

### Step 1: Determine the Selling Price (SP) of Each Horse
Both horses are sold for Rs 2380 each.

### Step 2: Calculate the Cost Price (CP) of the First Horse
The first horse is sold at a 20% profit.

Let the Cost Price of the first horse be \( CP_1 \).

Using the formula for selling price:
\[ SP = CP + \text{Profit} \]
The profit can be expressed as:
\[ \text{Profit} = 20\% \text{ of } CP_1 = \frac{20}{100} \times CP_1 = \frac{1}{5} \times CP_1 \]
Thus, we have:
\[ 2380 = CP_1 + \frac{1}{5} \times CP_1 \]
This can be rewritten as:
\[ 2380 = \frac{5}{5} \times CP_1 + \frac{1}{5} \times CP_1 = \frac{6}{5} \times CP_1 \]
To find \( CP_1 \):
\[ CP_1 = 2380 \times \frac{5}{6} = \frac{11900}{6} \approx 1983.33 \]

### Step 3: Calculate the Cost Price (CP) of the Second Horse
The second horse is sold at a 25% loss.

Let the Cost Price of the second horse be \( CP_2 \).

Using the formula for selling price:
\[ SP = CP - \text{Loss} \]
The loss can be expressed as:
\[ \text{Loss} = 25\% \text{ of } CP_2 = \frac{25}{100} \times CP_2 = \frac{1}{4} \times CP_2 \]
Thus, we have:
\[ 2380 = CP_2 - \frac{1}{4} \times CP_2 \]
This can be rewritten as:
\[ 2380 = \frac{4}{4} \times CP_2 - \frac{1}{4} \times CP_2 = \frac{3}{4} \times CP_2 \]
To find \( CP_2 \):
\[ CP_2 = 2380 \times \frac{4}{3} = \frac{9520}{3} \approx 3173.33 \]

### Step 4: Calculate Total Cost Price (CP) and Total Selling Price (SP)
Now, we can calculate the total cost price and total selling price:
\[ \text{Total CP} = CP_1 + CP_2 = 1983.33 + 3173.33 = 5156.66 \]
\[ \text{Total SP} = 2380 + 2380 = 4760 \]

### Step 5: Calculate Overall Profit or Loss
Now we can find the overall profit or loss:
\[ \text{Loss} = \text{Total CP} - \text{Total SP} = 5156.66 - 4760 = 396.66 \]

### Step 6: Calculate Loss Percentage
To find the loss percentage:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{\text{Total CP}}\right) \times 100 = \left(\frac{396.66}{5156.66}\right) \times 100 \approx 7.68\% \]

Thus, the overall loss percentage is approximately **7.68%**.