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Percentages Smart Math

[Smart Math] Percentages Problem 12

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

Percentages

Problem

Two typewriters were sold for $8000 each. The first was sold at a profit of 40% and the second at a loss of 40%. What was the cost price of the first typewriter?

  1. $2400.00
  2. $5612.33
  3. $3666.66
  4. $3256.50
  5. $5714.28

The Usual Method

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Let the cost price of the first typewriter be ‘x’.

Hence, selling price = 1.4x (including 40% profit)

\therefore 1.4x=8000

\therefore x=\frac{8000}{1.4}=5714.28

(Ans: 5)

Estimated Time to arrive at the answer = 60 seconds since the division will take some time.

Using Technique

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We know that selling price is 1.4 times the cost price. Hence, \frac{8000}{1.4} = the cost price.
\frac{8000}{1.4}=\frac{80000}{14}
We know that \frac{1}{7} = 0.1428…
\frac{80000}{14} is a division by 7 (Since, 14 is a multiple of 7). Hence, the numbers after the decimal point will be of the type .14… The only option matching this criterion is option ‘5’.

(Ans: 5)

Estimated Time to arrive at the answer = 10 seconds.

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