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Percentages Smart Math

[Smart Math] Percentages Problem 26

Here’s and example of a SMART MATH problem for PERCENTAGES.

Percentages

Problem

For a certain article if the discount is 10%, the profit is 10%. What is the profit if the discount is 5%?

  1. 5%
  2. 10%
  3. 13%
  4. 15%
  5. 16%

The Usual Method

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Let the cost price of the article be $100. Hence selling price = $110.

Hence marked price = \frac{110\times 100}{90}=100\times 1\frac{2}{9}

But when a discount of 5% is given, the marked price becomes \frac{95}{100}\times 100\times 1\frac{2}{9} = 95\times 1\frac{2}{9}

Hence Profit = 95\times 1\frac{2}{9} – 100 = 95\times \frac{11}{9}-100=\frac{1045}{9}-100=\frac{1045-900}{9}=\frac{145}{9}=16.11%

(Ans: 5)

Estimated Time to arrive at the answer = 60 seconds.

Using Technique

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Approximating, we can guesstimate that if the discount is 10%, the gap between the marked price and the cost price is 20%. Now if the discount is only 5% the gap between the cost price and selling price = 15%. However, the discount being calculated on the marked price and profit % on the cost price (cost price < marked price in this case since profit is generated), the actual gap will be slightly more than 15%. Hence 16%.

(Ans: 5)

Estimated Time to arrive at the answer = 10 seconds.
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