Question

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 ₹1860 as annual interest .However, had she interchanged the amount of investment in the two schemes , she would have received ₹20 more as annual interest . How much money did she invest in each scheme ?

Answer 1

Let the money invested in Scheme A be Rs x and that in Scheme B be Rs y.
$I=\frac{PRT}{100}$
So, Interest in scheme A = $\frac{8x}{100}$
Interest in scheme B = $\frac{9y}{100}$
Total annual interest = $\frac{8x}{100}$+$\frac{9y}{100}$ = 1860
⇒ 8x + 9y = 186000 .....(i)
After interchaning the amounts in the two schemes, the new total annual interest = $\frac{9x}{100}+\frac{8y}{100}$.
Now,
$\frac{9x}{100}+\frac{8y}{100}$ = 1860 + 20 = 1880
⇒ 9x + 8y = 188000 .....(ii)
Adding (i) and (ii), we get
17x + 17y = 374000
⇒ x + y = 22000 .....(iii)
Subtracting (i) from (ii), we get
x − y = 2000 .....(iv)
Adding (iii) and (iv), we get
2x = 24000
⇒ x = 12000
Puting x = 12000 in (iii), we get
12000 + y = 22000
⇒ y = 10000
So, the money invested in scheme A = Rs 12,000 and in scheme B = Rs 10,000.