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

**Problem**

**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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