Question

Joe invested $\$5000$ divided in two different schemes, Scheme A and Scheme B, at a simple interest rate of $5\%$ per annum and $3\%$ per annum, respectively. If the total amount of simple interest earned in $2$ years is $\$380$, find the amount invested in Scheme A.

• A. $\$200$
• B. $\$2000$
• C. $\$300$
• D. $\$3000$

Answer 1

The correct option is B $\$2000$

Amount invested $=\$5000$

Let the sum invested in scheme A be $\$x$ and that in scheme B be $\$(5000-x).$

Simple interest earned on scheme A $=x\times 0.05\times 2=\$0.1x$

Simple interest earned on Scheme B $=(5000-x)\times 0.03\times 2=0.06\times (5000-x)$

Total simple interest earned = simple interest earned on Scheme A + simple interest earned on Scheme B $(0.1x+0.06\times (5000-x\left)\right)$

Given, total interest earned is $\$380.$

So, $0.1x+0.06\times (5000-x)=380$

$\Rightarrow 4x+30000=38000$

$\Rightarrow 4x=38000-30000$

$\Rightarrow 4x=8000$

$\Rightarrow x=\frac{8000}{4}$

$\Rightarrow x=2000$

Hence, the amount invested in Scheme A is $\$2000.$