Question

the 8000 that he invested in fund a returned a 6% profit.the amount that he invested in fund b returned a 2% profit how much did he invest in fund b if both funds together returned a 3 % profit

Answer 1

Let

$\begin{gathered} x=\text{ the amount invested in fund b} \\ m=\text{ the profit from the fund a investment} \\ n=\text{ the profit from the fund b investment} \end{gathered}$

Therefore,

$\frac{m}{8000}=\frac{6}{100}$

Hence,

$m=\frac{6}{100}\times8000=6\times80=\text{ \ 480}$$\begin{gathered} \text{ Also} \\ n=0.02x------(1) \\ \frac{m+n}{8000+x}=0.03 \\ \text{therefore} \\ \frac{n+480}{8000+x}=0.03 \end{gathered}$

Thus

$n+480=0.03(8000+x)-----------------(2)$

Substituting equation(1) into equation(2), we have

$\begin{gathered} 0.02x+480=0.03(8000+x) \\ 0.02x+480=240+0.03x \\ \text{ Thus} \\ 0.03x-0.02x=480-240 \\ 0.01x=240 \\ x=\frac{240}{0.01}=2400 \end{gathered}$

Hence, the amount he invested is $2400