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Susan invested 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 investment in the two schemes, she would have received Rs. 20 more as annual interest. How much money did she invest in each scheme?
Given:
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. If she had interchanged the amount of investment in the two schemes, she would have received Rs. 20 more as annual interest.
To do:
We have to find the amount she invested in each scheme
Solution:
Let the amount invested in scheme A be $Rs.\ x$ and the amount invested in scheme B be $Rs.\ y$.
SI on $Rs.\ x$ at 8% per annum for 1 year $=Rs.\ \frac{x\times8\times1}{100}=Rs.\ \frac{8x}{100}$
SI on $Rs.\ y$ at 9% per annum for 1 year $=Rs.\ \frac{y\times9\times1}{100}=Rs.\ \frac{9y}{100}$
SI on $Rs.\ x$ at 9% per annum for 1 year $=Rs.\ \frac{x\times8\times1}{100}=Rs.\ \frac{9x}{100}$
SI on $Rs.\ y$ at 8% per annum for 1 year $=Rs.\ \frac{y\times9\times1}{100}=Rs.\ \frac{8y}{100}$
According to the question,
$\frac{8x}{100}+\frac{9y}{100}=1860$
$\frac{8x+9y}{100}=1860$
$8x+9y=1860(100)$......(i)
$\frac{9x}{100}+\frac{8y}{100}=1860+20$
$\frac{9x+8y}{100}=1880$
$9x+8y=1880(100)$......(ii)
Multiplying equation (i) by 8 on both sides, we get,
$8(8x+9y)=8(1860)(100)$
$64x+72y=14880(100)$.....(iii)
Multiplying equation (ii) by 9 on both sides, we get,
$9(9x+8y)=9(1880)(100)$
$81x+72y=16920(100)$.....(iv)
Subtracting equation (iii) from equation (iv), we get,
$(81x+72y)-(64x+72y)=16920(100)-14880(100)$
$81x-64x+72y-72y=2040(100)$
$17x=2040(100)$
$x=\frac{2040(100)}{17}$
$x=120(100)$
$x=12000$
Substituting $x=12000$ in equation (ii), we get,
$9(12000)+8y=1880(100)$
$108000+8y=188000$
$8y=188000-108000$
$8y=80000$
$y=\frac{80000}{8}$
$y=10000$
The money invested in scheme A is Rs. 12000 and the money invested in scheme B is Rs. 10000.
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