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Percentages Smart Math

[Smart Math] Percentages Problem 11

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

Percentages

Problem

A money lender lends $400 for 2 years and $200 for 3 years, at the same rate on simple interest and receives $70 as interest. What is the interest rate?

  1. 3.33%
  2. 4.00%
  3. 5.00%
  4. 8.33%
  5. 12.5%

The Usual Method

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Let ‘r’ be the rate of interest.

Hence, interest earned on $400 for 2 years = \frac{400\times 2\times r}{100}=8r

Similarly, interest earned on $200 for 3 years = \frac{200\times 3\times r}{100}=6r

Hence, total interest earned = 8r+6r = $70

\therefore 14r=70

\therefore r=\frac{70}{14}=5%

(Ans: 3)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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Interest on $400 for 2 years is equivalent to that for $200 for 4 years. Thus effectively $200 can be said to be lent for 4 + 3 = 7 years

\therefore Interest earned = \frac{200\times 7\times r}{100}=70

\therefore r=5%

(Ans: 3)

Estimated Time to arrive at the answer = 15 seconds.
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