Question

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. $5:3$
• B. $5:8$
• C. $4:8$
• D. $3:8$

Answer 1

The correct option is A $5:3$

Let $\$x$ is invested in the scheme with $4\%$ interest rate and $\$y$ in the scheme with $5\%$ interest rate.

Interest for the $1^{st}$ scheme for 1 year $=\$x\times \frac{4}{100}=\$0.04x$

And, interest for the $2^{nd}$ scheme for 1 year $=\$y\times \frac{5}{100}=\$0.05y$

$\therefore$ The total interest $=\$0.04x+\$0.05y$
$\Rightarrow 0.04x+0.05y=350...\left(a\right)$

Principal amount $=\$8,000$
$\Rightarrow x+y=8000...\left(b\right)$

Multiply (b) by $0.04$ and subtract from (a) to eliminate $x$.
$0.04x+0.05y-0.04(x+y)=350-0.04\left(8000\right)$
$\Rightarrow 0.01y=350-320=30$
$\Rightarrow y=\frac{30}{0.01}=\$3000$

Substituting $y$ in (b) we get,
$x+3000=8000$
$\Rightarrow x=\$5000$

$\therefore$ The ratio of investment $=\frac{x}{y}=\frac{5000}{3000}=5:3$