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Percentages Smart Math

[Smart Math] Percentages Problem 4

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

Percentages

Problem

Half of the consignment was sold at a profit of 10%. One third of the remaining is sold at a loss of 12% and the remaining at a loss of 6%. What would be the overall gain or loss % if the value of the total consignment was $8850?

  1. 2.5% loss
  2. 3% gain
  3. 1% gain
  4. 1.5% loss
  5. None of these

The Usual Method

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First you find out the fractional values of the parts

i.e. \frac{1}{2}\times 8850=4425, \frac{1}{3}\times 8850=2950 and \frac{1}{6}\times 8850=1475.

Now applying the respective percentages to it,

4425 x 10% = 442.5 (gain)

1475 x 12% = 177.0 (loss)

2950 x 6% = 177.0 (loss)

Hence, the net effect is 442.5 – 177.0 – 177.0 = 88.50 (gain)

Thus there is a net gain of \frac{88.50}{8850}\times 100 = 1% gain

(Ans: 3)

Estimated Time to arrive at the answer = 75 seconds.

Using Technique

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Simply get the fractions and multiply with the respective percentages as shown below:

\frac{1}{2}\times 10-\frac{1}{6}\times 12-\frac{1}{3}\times 6=5-2-2=1% (gain) i.e option ‘3’.

This is possible since we are only finding the net percentage and so the absolute value of $8850 cancels out and so is eliminated.

(Ans: 3)

Estimated Time to arrive at the answer = 15 seconds.
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