Question

Question 12
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 investments in the two schemes, she would have received Rs. 20 more as annual interest. How much money did she invest in each scheme?

Answer 1

Let the amount of investments in schemes. A and B be Rs. x and Rs. y. respectively
Case I interest at the rate of $8\%$ per annum on scheme A + interest at the rate of $9\%$ percent annum on scheme B = Total amount received
$\Rightarrow \frac{x\times 8\times 1}{100}+\frac{y\times 9\times 1}{100}=Rs.1860[\therefore simpleinterest=\frac{principle\times rate\times time}{100}]$
$\times 8x+9y=186000$
Case II interest at the rate of $9\%$ per annum on scheme A + interest at the rate of $8\%$ per annum on scheme B = Rs. 20 more as annual interest
$\Rightarrow \frac{x\times 9\times 1}{100}+\frac{y\times 8\times 1}{100}=Rs20+Rs.1860$
$\Rightarrow \frac{9x}{100}+\frac{8y}{100}=1880$
9x + 8y = 188000
On multiplying Eq. (i) by 9 and Eq. (ii) by 8 and then subtracting them, we get
72x + 81y = 9 $\times$ 186000

72x + 64y = 8 $\times$ 188000

$\Rightarrow 17y=100\left[\right(9\times 186)-(8\times 188\left)\right]$

= 1000 (1674 – 1504) = 1000 $\times$ 170

17y = 170000 $\Rightarrow$ y = 10000

On putting the value of y in Eq (i), we get

8x + 9 $\times$ 10000 = 186000

$\Rightarrow$ 8x = 186000 – 90000

$\Rightarrow$ 8x = 96000

$\Rightarrow$ x = 12000
Hence, she invested Rs. 12000 and Rs. 10000 in two schemes A and B, respectively