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[Smart Math] Percentages Problem 11

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

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 [contentblock id=google-adsense-post] 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

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 = $\frac{200\times 7\times r}{100}=70$
$\therefore r=5$%