A principal amount of $8,000 was partly invested in two schemes with an annual interest rate of 4% and 5%, respectively. At the end of the year, the total interest is $350. Find the ratio of investment.
A
5:3
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B
5:8
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C
4:8
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D
3:8
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Solution
The correct option is A5:3 Let $x is invested in the scheme with 4% interest rate and $y in the scheme with 5% interest rate.
Interest for the 1st scheme for 1 year =$x×4100=$0.04x
And, interest for the 2nd scheme for 1 year =$y×5100=$0.05y
∴ The total interest =$0.04x+$0.05y ⇒0.04x+0.05y=350...(a)
Principal amount =$8,000 ⇒x+y=8000...(b)
Multiply (b) by 0.04 and subtract from (a) to eliminate x. 0.04x+0.05y−0.04(x+y)=350−0.04(8000) ⇒0.01y=350−320=30 ⇒y=300.01=$3000
Substituting y in (b) we get, x+3000=8000 ⇒x=$5000