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Algebra Smart Math

[Smart Math] Algebra Problem 21

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

Algebra

Problem

A man incurred a loss by selling a book for $60. Had he sold it for $75, his gain would have been 4 times the former loss. Find the cost price of the book.

  1. $75
  2. $63
  3. $65
  4. $69
  5. $80

The Usual Method

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Let the cost price of the book be $‘x’.

Hence loss incurred by selling it at $60 = $(x – 60)

Gain accrued by selling it at $75 = $(75 – x)

Since gain = 4 times loss, we get:

(75 – x) = 4(x – 60)

\therefore 75-x=4x-240

\therefore 5x=315

\therefore x=\frac{315}{5}= $63

(Ans: 2)

Estimated Time to arrive at the answer = 60 seconds.

Using Technique

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Difference between the selling prices = 75 – 60 = 15.

15 when broken up in the ratio of 1 : 4 (1 being loss and 4 being gain), we get loss = \frac{15\times 1}{1+4}=3. So cost price = 60 + 3 = $63

Similarly, from the gain side, gain = \frac{15\times 4}{1+4}=12. Hence cost price = 75 – 12 = $63

(Ans: 2)

Estimated Time to arrive at the answer = 15 seconds.
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