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

(A) Let the amount invested in schemes $A$ and $B$ be $Rs.\, x$ and $Rs.\, y,$ respectively.
$Case \, I$: Interest at $8 \%$ per annum on scheme $A$ + Interest at $9 \%$ per annum on scheme $B = 1860$.
$\Rightarrow \frac{8x}{100} + \frac{9y}{100} = 1860 \Rightarrow 8x + 9y = 186000 \quad \dots(i)$
$Case \, II$: If amounts are interchanged,interest is $1860 + 20 = 1880$.
$\Rightarrow \frac{9x}{100} + \frac{8y}{100} = 1880 \Rightarrow 9x + 8y = 188000 \quad \dots(ii)$
Multiply $(i)$ by $8$ and $(ii)$ by $9$:
$64x + 72y = 1488000 \quad \dots(iii)$
$81x + 72y = 1692000 \quad \dots(iv)$
Subtract $(iii)$ from $(iv)$:
$(81x - 64x) = 1692000 - 1488000$
$17x = 204000 \Rightarrow x = 12000$
Substitute $x = 12000$ in $(i)$:
$8(12000) + 9y = 186000$
$96000 + 9y = 186000$
$9y = 90000 \Rightarrow y = 10000$
Thus,she invested $Rs.\, 12000$ in scheme $A$ and $Rs.\, 10000$ in scheme $B$.