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Percentages Smart Math

[Smart Math] Percentages Problem 25

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

Percentages

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?

  1. 50/3
  2. 100/3
  3. 30/2
  4. 50/4
  5. 100/4

The Usual Method

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

Hence cost price of A = \frac{45000}{0.9}=50000

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 = \frac{15000}{45000}\times 100=\frac{100}{3}%

(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 = \frac{30}{90}\times 100=\frac{100}{3}%

(Ans: 2)

Estimated Time to arrive at the answer = 15 seconds.
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