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# [Smart Math] Percentages Problem 26

Here’s and example of a SMART MATH problem for 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

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.