A man sells his new brand car for N420,000 at a gain of 15%. What did it cost him?

Analysis

To solve this problem, we need to understand the relationship between Cost Price (CP), Selling Price (SP), and Percentage Gain.

When an item is sold at a gain, the Selling Price is the sum of the Cost Price and the profit made. Since the gain is expressed as a percentage of the Cost Price, we use the following formula: Selling Price = Cost Price + (Percentage Gain × Cost Price) Or simply: Selling Price = Cost Price × (1 + Gain%)

Concept

• Cost Price (CP): The original amount the man paid for the car.
• Selling Price (SP): The amount he sold it for (N420,000).
• Gain Percentage: 15% (which is 0.15 in decimal form).

Step-by-Step Solution

1. Set up the equation: Let the Cost Price be $x$. $x + 0.15x = 420,000$

2. Combine the terms: $1.15x = 420,000$

3. Solve for $x$: $x = \frac{420,000}{1.15}$

4. Perform the division: $x = 365,217.391...$

Rounding to the nearest whole number, we get N365,217.

Conclusion

Comparing our result to the given options, it matches option B.

Exam Tip

When dealing with "gain" or "loss" percentage questions, always remember that the percentage is calculated on the Cost Price, not the Selling Price. A common mistake students make is calculating 15% of N420,000 and subtracting it; avoid this! Always set up your equation as $CP \times (1 \pm \text{rate}) = SP$.