A man sells two horses for Rs. 38. The cost price of the first of equal to the selling price of the second . If the first is sold at `10%` loss and the second at `25%` gain, what is his total gain or loss (in rupees)?

Options

A. 0.2
B. 20
C. 2
D. 1

Answer

To solve the problem step by step, we will denote the following:

- Let the cost price of the first horse be \( CP_1 \).
- Let the cost price of the second horse be \( CP_2 \).
- Let the selling price of the first horse be \( SP_1 \).
- Let the selling price of the second horse be \( SP_2 \).

### Step 1: Set up the equations based on the problem statement

From the problem, we know:

1. The total selling price of the two horses is Rs. 38:
\[ SP_1 + SP_2 = 38 \]

2. The cost price of the first horse is equal to the selling price of the second horse:
\[ CP_1 = SP_2 \]

3. The first horse is sold at a 10% loss:
\[ SP_1 = CP_1 - 0.1 \times CP_1 = 0.9 \times CP_1 \]

4. The second horse is sold at a 25% gain:
\[ SP_2 = CP_2 + 0.25 \times CP_2 = 1.25 \times CP_2 \]

### Step 2: Substitute \( SP_2 \) in terms of \( CP_1 \)

From equation 2, we can substitute \( SP_2 \) in terms of \( CP_1 \):
\[ SP_2 = CP_1 \]

### Step 3: Substitute \( SP_1 \) and \( SP_2 \) into the total selling price equation

Now, substituting \( SP_1 \) and \( SP_2 \) into the total selling price equation:
\[ 0.9 \times CP_1 + CP_1 = 38 \]
\[ 1.9 \times CP_1 = 38 \]

### Step 4: Solve for \( CP_1 \)

Now, we can solve for \( CP_1 \):
\[ CP_1 = \frac{38}{1.9} = 20 \]

### Step 5: Find \( SP_1 \) and \( SP_2 \)

Now that we have \( CP_1 \):
- Calculate \( SP_1 \):
\[ SP_1 = 0.9 \times CP_1 = 0.9 \times 20 = 18 \]

- Since \( CP_1 = SP_2 \), we have:
\[ SP_2 = 20 \]

### Step 6: Calculate \( CP_2 \)

Now, we can find \( CP_2 \) using the equation for \( SP_2 \):
\[ SP_2 = 1.25 \times CP_2 \]
Substituting \( SP_2 = 20 \):
\[ 20 = 1.25 \times CP_2 \]
\[ CP_2 = \frac{20}{1.25} = 16 \]

### Step 7: Calculate total cost price and total selling price

Now we can calculate the total cost price and total selling price:
- Total cost price:
\[ Total \, CP = CP_1 + CP_2 = 20 + 16 = 36 \]

- Total selling price:
\[ Total \, SP = SP_1 + SP_2 = 18 + 20 = 38 \]

### Step 8: Calculate total gain or loss

Finally, we can calculate the total gain or loss:
\[ Total \, Gain = Total \, SP - Total \, CP = 38 - 36 = 2 \]

Thus, the man has a total gain of Rs. 2.