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

**Problem**

**Problem**

An item is sold at a profit of 10%. Had it been bought for 10% less and sold for $10 less, the profit would have been 20%. What is the cost price of the item?

- 100
- 1000
- 500
- 200
- 50

**The Usual Method**

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Let the cost price of the article be $‘*x*’.

Hence selling price = 1.1*x*

New cost price = 0.9*x*

New selling price = 1.1*x* – 10

Hence profit at new selling price on new cost price =

(As given in the question)

**(Ans: 3)**

*Estimated Time to arrive at the answer = 45 seconds.*

**Using Technique**

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Note that the new cost price will be 90% of the original cost price. Hence the denominator in the formula to find profit % (Profit % = ) will be a multiple of 9 (in this case 0.9*x*)

Also note that since the new percentage profit being 20% – a whole number, the numerator (*SP* – *CP*) should also be a multiple of 9. Checking the options as follows:

Option New SP New CP Difference Remarks

a. 110 – 10 = 100 90 10 Not a multiple of 9

b. 1100 – 10 = 1090 900 190 Not a multiple of 9

c. 550 – 10 = 540 450 90 Multiple of 9

No need to check further as there cannot be more than one correct answer!

**(Ans: 3)**

*Estimated Time to arrive at the answer = 30 seconds.*

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