Question

You have $Rs.12,000$ and you want to invest it in two schemes yielding $10\%$ and $15\%$ interest . How much amount should be invested in each schemes so that you get overall $12\%$ of interest .

Answer 1

Let the amount to be saved at $10\%$ be $x$

Let the amount to be saved at $15\%$ be $y$

According to question,

$x+y=\mathrm{12000.....}\left(1\right)$ and

$10\%\text{of}x+15\%\text{of}y=12\%\text{of}12000$

$\Rightarrow \frac{10}{100}x+\frac{15}{100}y=\frac{12}{100}\times 12000$

$\Rightarrow 10x+15y=\mathrm{144000...}\left(2\right)$

The equation $\left(1\right)\times 10\Rightarrow 10x+10y=\mathrm{120000...}\left(3\right)$

Now, equation$\left(2\right)-\left(3\right)$

$\Rightarrow 15y-10y=144000-120000$

$\Rightarrow 5y=24000$

$\Rightarrow y=\frac{24000}{5}=4800$

Substitute $y=4800$ value in $x+y=12000$

$\Rightarrow x+4800=12000$

$\Rightarrow x=12000-4800=7200$

The amount saved at $10\%$ = $Rs.7200$

The amount saved at $15\%$ = $Rs.4800$.