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Percentages Smart Math

[Smart Math] Percentages Problem 35

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

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

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\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

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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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