A man bought two old scooters for Rs. 18000. By selling one at a profit of `25%` and the other at a loss of `20%`, he neither gains nor loses. Find the cost price of each scooter.

Options

A. 12000, 6000
B. 8000, 10000
C. 11000, 7000
D. 13000, 5000

Answer

To solve the problem step by step, we need to find the cost price of each scooter given that the total cost price of both scooters is Rs. 18,000, and the selling prices result in no overall profit or loss.

### Step 1: Define Variables
Let the cost price of the first scooter be \( x \). Therefore, the cost price of the second scooter will be \( 18000 - x \).

**Hint:** Define variables for unknowns to simplify calculations.

### Step 2: Calculate Selling Prices
The selling price of the first scooter, sold at a profit of 25%, can be calculated as:
\[ \text{Selling Price of First Scooter} = x + \frac{25}{100} \times x = x + 0.25x = 1.25x \]

The selling price of the second scooter, sold at a loss of 20%, can be calculated as:
\[ \text{Selling Price of Second Scooter} = (18000 - x) - \frac{20}{100} \times (18000 - x) = (18000 - x) - 0.2(18000 - x) = 0.8(18000 - x) \]

**Hint:** Use profit and loss formulas to calculate selling prices from cost prices.

### Step 3: Set Up the Equation
Since the man neither gains nor loses, the total selling price of both scooters equals the total cost price:
\[ 1.25x + 0.8(18000 - x) = 18000 \]

**Hint:** Set up an equation based on the condition provided in the problem.

### Step 4: Simplify the Equation
Now, simplify the equation:
\[ 1.25x + 14400 - 0.8x = 18000 \]
Combine like terms:
\[ (1.25x - 0.8x) + 14400 = 18000 \]
\[ 0.45x + 14400 = 18000 \]

**Hint:** Combine like terms to make the equation easier to solve.

### Step 5: Solve for \( x \)
Subtract 14400 from both sides:
\[ 0.45x = 18000 - 14400 \]
\[ 0.45x = 3600 \]
Now, divide both sides by 0.45 to find \( x \):
\[ x = \frac{3600}{0.45} = 8000 \]

**Hint:** Isolate the variable to find its value.

### Step 6: Find the Cost Price of the Second Scooter
Now that we have the cost price of the first scooter, we can find the cost price of the second scooter:
\[ \text{Cost Price of Second Scooter} = 18000 - x = 18000 - 8000 = 10000 \]

**Hint:** Use the total cost price to find the remaining unknown.

### Conclusion
The cost price of the first scooter is Rs. 8000, and the cost price of the second scooter is Rs. 10000.

**Final Answer:**
- Cost Price of First Scooter: Rs. 8000
- Cost Price of Second Scooter: Rs. 10000