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# [Smart Math] Percentages Problem 12

Here’s and example of a SMART MATH problem for 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

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

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’.