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

**Problem**

**Problem**

A sells B a piece of furniture for $45,000 at a loss of 10% B sells it to C at a price which would have given A a profit of 20%. What percent does B gain?

- 50/3
- 100/3
- 30/2
- 50/4
- 100/4

**The Usual Method**

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Selling price of A = Cost price of B = $45000

Hence cost price of A =

Selling price of A with 20% profit = Selling price of B = 50000 x 1.2 = 60000

Profit of B = Selling price of B – Cost price of B

= $60,000 – $45,000 = $15,000

Hence profit percent of B = %

**(Ans: 2)**

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

**Using Technique**

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Observe that if A’s cost price would have been $100, his selling price with 10% loss would be $90 and his selling price with 20% gain would be $120. Hence gain = 120 – 90 = 30

Selling price of A with 10% loss = Cost price of B = $90.

Hence Profit %for B = %

**(Ans: 2)**

*Estimated Time to arrive at the answer = 15 seconds.*

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