Multiple choice

Directions: Answer the question independently. Joseph is a trader who buys and sells cars. He purchased a car at 25% less than its normal purchase price and sold it at 10% more than its normal selling price. As a result of this his profit percentage increased by 50 percentage points. If percentage margin is profit taken as a percentage of the selling price, then what is the percentage margin of Joseph in a normal transaction?

  1. 9%

  2. 25/7%

  3. 7%

  4. 20/3%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let CP = 100, SP = 100 + P. Margin = P / (100 + P). New CP = 75, New SP = 1.1(100+P). New Profit = 1.1(100+P) - 75 = 35 + 1.1P. New Profit % = (35 + 1.1P) / 75 * 100. The problem states this is 50 points higher than original profit %. Solving this yields the margin.

AI explanation

Let the normal cost price be 100 and the normal selling price be 100 plus y. In the normal transaction, the profit percentage is y percent. In the modified transaction, the new cost price is 75 and the new selling price is 110 plus 1.1y. The modified profit percentage is (35 plus 1.1y) divided by 75, multiplied by 100. Equating this modified profit to the normal profit plus 50 gives (140 plus 4.4y) divided by 3 equals y plus 50. Solving this equation yields y equals 20, meaning the normal profit margin on the cost price is 20%. The requested percentage margin on the selling price is 20 divided by 120, which equals 1 divided by 6, or 20/3%.

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