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# [Smart Math] Algebra Problem 21

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.

1. $75 2.$63
3. $65 4.$69
5. $80 ### The Usual Method [contentblock id=google-adsense-post] Let the cost price of the book be$‘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 [contentblock id=google-adsense-post] 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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