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# [Smart Math] Percentages Problem 4

Here’s and example of a SMART MATH problem for PERCENTAGES. 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 [contentblock id=google-adsense-post] 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 [contentblock id=google-adsense-post] 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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