A public car dealer marked up the cost of a car at 30% in an attempt to make 20% gross profit. Due to the…

1. Analyze the Question

We need to determine the final percentage profit or loss after a series of price adjustments.

• Step 1: The dealer marks up the cost price by 30%.
• Step 2: The dealer then offers a 20% discount on the new marked price.
• Goal: Find the final percentage change relative to the original cost price.

2. Explain the Concept

To solve this, we use the concept of successive percentage changes. It is easiest to assume the original cost price ($CP$) is 100 units. This makes percentage calculations straightforward.

• Mark-up: Increasing a value by $x\%$ means multiplying by $(1 + \frac{x}{100})$.
• Discount: Decreasing a value by $y\%$ means multiplying by $(1 - \frac{y}{100})$.

3. Show the Solution

Let the Cost Price ($CP$) = 100.

Step 1: Calculate the Marked Price ($MP$) The dealer marks up the price by 30%: $MP = CP + (30\% \text{ of } CP)$ $MP = 100 + 30 = 130$

Step 2: Calculate the Selling Price ($SP$) The dealer offers a 20% discount on the marked price ($MP$): Discount = $20\% \text{ of } 130$ Discount = $0.20 \times 130 = 26$

$SP = MP - \text{Discount}$ $SP = 130 - 26 = 104$

Step 3: Calculate the Profit or Loss Profit/Loss = $SP - CP$ Profit/Loss = $104 - 100 = 4$

Since the result is positive, it is a profit. Percentage Profit = $(\frac{\text{Profit}}{CP}) \times 100\%$ Percentage Profit = $(\frac{4}{100}) \times 100\% = 4\%$

4. Identify the Answer

Comparing our result to the options provided: A. 3% B. 2% C. 4% D. 1%

The correct option is C.

5. Exam Tip

When dealing with successive percentage changes (like mark-ups and discounts), you can use the formula: Final Change = $a + b + \frac{ab}{100}$ Where $a$ is the first change (+30) and $b$ is the second change (-20). Calculation: $30 + (-20) + \frac{30 \times (-20)}{100}$ $= 10 + (\frac{-600}{100})$ $= 10 - 6 = 4\%$ This shortcut saves time in the exam hall!