Question

A man invested an amount at 10% per annum and another amount at 8% per annum simple interset.Thus,he received Rs.1350 as annual interest.Had he interchanged the amounts invested,he would have received Rs.45 less as interest.What amounts did he invest at different rates?

Answer 1

lets call bank A giving 10% interest per annum

and bank B giving 8% per annum

now Case 1 :

Rs. x in bank A and Rs. y in bank B

so principal amount in bank A = Rs. x
rate = 10 % = $\frac{10}{100}$
time = 1 year
so interest in his investment = $\frac{10x}{100}=\frac{x}{10}$

while in bank B
principal amount = Rs. y
rate = 8% = $\frac{8}{100}$
time = 1 yr

so interest on his investment = $\frac{8y}{100}=\frac{2y}{25}$
A/Q = total interest he gets = $\frac{x}{10}+\frac{2y}{25}=1350$
multiply through out with 250
25x+20y=337500
divide with 5
5x+4y=67500.........(1)
Case 2:

Principal amount in bank A = Rs. y
rate = 10%=$\frac{10}{100}$
time = 1 yr

so simple interest = 10y/100 = y/10

similarly bank B princpal amount = Rs. x
rate = 8% = $\frac{8}{100}$
time = 1 yr

so simple interest =$\frac{2x}{25}$

A/Q = total interest = $\frac{y}{10}+\frac{2x}{25}$ = 1350 - 45 = 1305
multiply with 250
25y+20x=326250
divide by 5
5y+4x=65250......(2)



5x+4y=67500.........(1)
4x+5y=65250......(2)

$\left(1\right)\times 4$ is 20x+16y=270000 ........(3)
$\left(2\right)\times 5$ is 20x+25y=326250 .........(4)

(4)-(3)
0x+9y=56250
y=$\frac{56250}{9}$=6250

so (1) implies
5x+4y=67500
$5x+4\times 6250=675005x+25000=675005x=42500x=\frac{42500}{5}x=8500$

from (2) , $y=\frac{65250-4x}{5}y=\frac{65250-4\times 8500}{5}y=6250$