Here’s and example of a SMART MATH problem for 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.
- $75
- $63
- $65
- $69
- $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)
$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 = . So cost price = 60 + 3 = $63
Similarly, from the gain side, gain = . Hence cost price = 75 – 12 = $63
(Ans: 2)
Estimated Time to arrive at the answer = 15 seconds.
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