Here’s and example of a SMART MATH problem for 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?
- $3333
- $6000
- $6666
- $7500
- $10000
The Usual Method
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Let the original sum be $x.
Thus, invested at 3% gives an interest of
Similarly, invested at 6% gives an interest of
and the remaining, =
is invested at 8% gives an interest of
Hence, total earnings =
Since,
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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