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# [Smart Math] Percentages Problem 35

Hereâ€™s and example of a SMART MATH problem for PERCENTAGES.

### Problem

Some goods together cost \$35849.50. $\frac{3}{4}$th of them are sold at a profit of 30%. At what profit / loss should the remaining be sold to realize 20% gain on the whole?

1. 15% loss
2. 10% loss
3. 5% loss
4. 10% gain
5. 15% gain

### The Usual Method

$\frac{3}{4}$ of 35849.50 = $\frac{3}{4}\times 35849.50=26887.125$

30% profit = $\frac{30}{100}\times 26887.125=8066.13$

20% profit on whole = $\frac{20}{100}\times 35849.50=7169.9$

$\therefore$ if x% be the loss / gain on $\frac{1}{4}$ th of 35849.50 = $\frac{x}{100}\times \frac{1}{4}\times 35849.50=\frac{x}{100}\times 8962.375$

Then, $\frac{x}{100}\times 8962.375+8066.13=7169.9$

$\therefore \frac{x\times 8962.375}{100}=-896.23$

$\therefore x=-\frac{89623}{8962.375}\approx -10$

Hence 10% loss.

(Ans: 2)

Estimated Time to arrive at the answer = 60 seconds.

### Using Technique

Irrespective of the original amount, you can simply solve as follows:

30 + x = 20

$\therefore x=-10$. Hence 10% loss.

(Ans: 2)

Estimated Time to arrive at the answer = 5 seconds.
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## 2 replies on “[Smart Math] Percentages Problem 35”

shakyarajsays:

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shakyarajsays:

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