Mani bought two horses at 20,000 each. He sold one horse at 15% gain. But he had to sell the second horse at a loss. If he had suffered a loss of 1800 on the whole transaction, find the selling price of the second horse.

Options

A. 10000
B. 15000
C. 15200
D. 12000

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Calculate the Selling Price of the First Horse
Mani bought two horses for ₹20,000 each. Therefore, the cost price (CP) of the first horse is:
\[ CP_{\text{first horse}} = ₹20,000 \]

He sold the first horse at a gain of 15%. To find the selling price (SP) of the first horse, we use the formula:
\[ SP = CP + \text{Gain} \]
Where Gain is calculated as:
\[ \text{Gain} = \frac{15}{100} \times CP_{\text{first horse}} \]
Calculating the gain:
\[ \text{Gain} = \frac{15}{100} \times 20,000 = ₹3,000 \]
Now, calculating the selling price:
\[ SP_{\text{first horse}} = 20,000 + 3,000 = ₹23,000 \]

### Step 2: Calculate the Total Loss
According to the problem, Mani suffered a total loss of ₹1,800 on the whole transaction. Since he bought two horses for ₹20,000 each, the total cost price (CP) for both horses is:
\[ CP_{\text{total}} = 20,000 + 20,000 = ₹40,000 \]

Now, if he incurred a loss of ₹1,800, the total selling price (SP) of both horses is:
\[ SP_{\text{total}} = CP_{\text{total}} - \text{Loss} \]
Calculating the total selling price:
\[ SP_{\text{total}} = 40,000 - 1,800 = ₹38,200 \]

### Step 3: Calculate the Selling Price of the Second Horse
Let the selling price of the second horse be \( SP_{\text{second horse}} \). We know that:
\[ SP_{\text{total}} = SP_{\text{first horse}} + SP_{\text{second horse}} \]
Substituting the known values:
\[ 38,200 = 23,000 + SP_{\text{second horse}} \]
Now, solving for \( SP_{\text{second horse}} \):
\[ SP_{\text{second horse}} = 38,200 - 23,000 \]
\[ SP_{\text{second horse}} = ₹15,200 \]

### Conclusion
The selling price of the second horse is ₹15,200.

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