A trader bought two horses for 19,500. He sold one at a loss of 20% and the other at a profit of 15%. If the selling price of each horse is the same, then their cost price are respectively.

Options

A. 10,000 and 9,500
B. 11,500 and 8,000
C. 12,000 and 7,500
D. 10,500 and 9,000

Answer

To solve the problem step by step, we will denote the cost price of the first horse as \( X \) and the cost price of the second horse as \( Y \).

### Step 1: Set up the equations
The total cost price of both horses is given as:
\[ X + Y = 19,500 \]

### Step 2: Calculate the selling price of the first horse
The first horse is sold at a loss of 20%. Therefore, the selling price (SP) of the first horse can be calculated as:
\[ SP_1 = X - 0.20X = 0.80X = \frac{80X}{100} \]

### Step 3: Calculate the selling price of the second horse
The second horse is sold at a profit of 15%. Therefore, the selling price of the second horse can be calculated as:
\[ SP_2 = Y + 0.15Y = 1.15Y = \frac{115Y}{100} \]

### Step 4: Set the selling prices equal
Since the selling prices of both horses are the same, we can set the two equations equal to each other:
\[ 0.80X = 1.15Y \]

### Step 5: Rearrange the equation
From the equation \( 0.80X = 1.15Y \), we can express \( Y \) in terms of \( X \):
\[ Y = \frac{0.80X}{1.15} \]

### Step 6: Substitute \( Y \) in the total cost price equation
Now, substitute \( Y \) in the total cost price equation:
\[ X + \frac{0.80X}{1.15} = 19,500 \]

### Step 7: Solve for \( X \)
To solve for \( X \), we first find a common denominator:
\[ X + \frac{0.80X}{1.15} = \frac{1.15X + 0.80X}{1.15} = \frac{1.95X}{1.15} \]
So, we have:
\[ \frac{1.95X}{1.15} = 19,500 \]
Multiplying both sides by 1.15:
\[ 1.95X = 19,500 \times 1.15 \]
Calculating the right side:
\[ 1.95X = 22,425 \]
Now, divide both sides by 1.95:
\[ X = \frac{22,425}{1.95} = 11,500 \]

### Step 8: Calculate \( Y \)
Now that we have \( X \), we can find \( Y \):
\[ Y = 19,500 - X = 19,500 - 11,500 = 8,000 \]

### Final Result
The cost prices of the horses are:
- Cost price of the first horse \( X = 11,500 \)
- Cost price of the second horse \( Y = 8,000 \)