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Percentages Smart Math

[Smart Math] Percentages Problem 10

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

Percentages

Problem

Of a certain sum, 1/3rd is invested at 3%, 1/6th at 6% and the rest at 8%. If the annual simple interest from this entire amount is $600, what is the original sum?

  1. $3333
  2. $6000
  3. $6666
  4. $7500
  5. $10000

The Usual Method

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Let the original sum be $x.

Thus, \frac{1}{3}x invested at 3% gives an interest of \frac{1}{3}x\times \frac{3}{100}\times 1=\frac{1}{100}x

Similarly, \frac{1}{6}x invested at 6% gives an interest of \frac{1}{6}x\times \frac{6}{100}\times 1=\frac{1}{100}x and the remaining, = \left[ 1-\left( \frac{1}{3}+\frac{1}{6} \right) \right]x=\frac{1}{2}x is invested at 8% gives an interest of \frac{1}{2}x\times \frac{8}{100}\times 1=\frac{4}{100}x

Hence, total earnings = \frac{1}{100}x+\frac{1}{100}x+\frac{4}{100}x=\frac{6}{100}x

Since, \frac{6}{100}x=600

x = $10,000

(Ans: 5)

Estimated Time to arrive at the answer = 60 seconds.

Using Technique

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Instead of taking the initial figure as ‘x’, to avoid working with fractions, assume the figure as $300.

Thus 1/3rd of $300 = $100 @ 3% gives interest of $3

And 1/6th of $300 = $50 @ 6% gives interest of $3

And the balance Rs300 – $100 – $50 = $150 @ 8% gives interest of $12

Thus total interest earned = 3 + 3 + 12 = $18.

For a total amount of $300, the interest earned = $18,

For what total amount would the interest = $600

Doing cross multiplication, we get $10,000

(Ans: 5)

Estimated Time to arrive at the answer =30 seconds.
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