Question

A person invested some money at $12\%$ simple interest and some other amount at $10\%$ simple interest. He received yearly interest of Rs. $1300$. If he had interchanged the amounts, he would have received Rs. $40$ more as yearly interest. Find the total money person have in starting

Answer 1

Let money for part $1$ be ${}^{\prime }{x}^{\prime }$ and part $2$ be ${}^{\prime }{y}^{\prime }$

For Part $1$

$P=xR=12\%T=1S.I=\frac{PRT}{100}=\frac{x\times 12\times 1}{100}=\frac{3x}{25}$

For Part $2$

$P=yR=10\%T=1S.I=\frac{PRT}{100}=\frac{y\times 10\times 1}{100}=\frac{y}{10}$

ATP, $\frac{3x}{25}+\frac{y}{10}=1300\Rightarrow 6x+5y=6500⟶\left(1\right)$

For Part $1$

$S.I$=$\frac{y\times 12\times 1}{100}$ =$\frac{3y}{25}$

For Part $2$

$S.I=\frac{x\times 10\times 1}{100}=\frac{x}{10}$

ATP, $\frac{3y}{25}+\frac{x}{10}=1340\Rightarrow 6y+5x=6700⟶\left(2\right)$

Substituting ${}^{\prime }{x}^{\prime }$ from $eq\left(1\right)$ in $eq\left(2\right)$

$6y+5\left(\frac{65000-5y}{6}\right)=67000\Rightarrow 36y-25y+32500=402000\Rightarrow 11y=65000\Rightarrow y=7000\therefore x=\frac{65000-5\times 7000}{6}x=5000$

$\therefore$ Total Money that person had $=x+y=Rs.(5000+7000)=Rs.12000$.