Question

Susan invested certain amount of money in two scheme $A$ and $B$, which offer interest at the rate of $8$% per annum and $9$% per annum, respectively. She received Rs $1860$ as as annual interest. However, had she interchanged the amount of investment in the two scheme, she would have received, Rs $20$ more as annual interest. How much money did she invest in each scheme?

Answer 1

let the money invested in scheme $A=Rsx$
and the money invested in scheme$B$ = $Rsy$
Case I : Susan invested $rsx$ at $8$ % p.a. + Susan invested $Rsy$at $9$ % at p.a. =$1860$
$\Rightarrow \frac{x\times 8\times 1}{100}+\frac{y\times 9\times 1}{100}=1860$
$\Rightarrow 8x+9y=186000....\left(ii\right)$
case II : Interchanging the amount in schemes $A$ and $B$ we have
$\frac{9\times x}{100}+\frac{8\times y}{100}=(1860+20)$
$\Rightarrow 9x+8y=188000....\left(ii\right)$
Adding $\left(i\right)$ and $\left(ii\right)$ we get
$9x+8y=188000....\left(ii\right)$
$8x+9y=186000......\left(i\right)$
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$17x+17y=374000$
$\Rightarrow x+y=\mathrm{22000......}\left(iii\right)$
on subtracting $\left(i\right)$ and $\left(ii\right)$ we get $x-y=2000....\left(iv\right)$
Now, $x-y=2000.....\left(iv\right)$
$x+y=\mathrm{22000........}\left(iii\right)$
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$2x=24000$ [adding (iv) and (iii) ]
$\Rightarrow x=rs12000$
Now $x+y=22000\left[from\right(iii\left)\right]$
$\Rightarrow y=22000-12000$
$\Rightarrow y=Rs10,000$
hence the amount invested in schemes $A$ and $B$ are $Rs12000$ and $Rs10,000$ Respectively.