Question

A sum of money lent at SI amounts to 7500 Rs in 5 years and 9500 Rs in 9 years. Find the sum of money and the rate of the interest.​

Answer 1

Answer:

let X be the sum of money and let r be the rate of interest.

then, Amount A = X(1+rt)

when amount is 7500

=>7500 = X(1+5r)

=7500/X = 1+5r

=>5r = (7500/X)-1

=>r= (1500/X)-0.2-----------(1)

when amount is 9500

=>9500 = X(1+9r)

=>9500/X = 1+9r

=>9r=(9500/X)-1

=>r = (9500/(9X))-(1/9)----------(2)

comparing eqn 1 and 2

(1500/X)-0.2 = (9500/(9X))-(1/9)

=>1500-0.2X = (9500-X)/9

=>13500-1.8X = 9500-X

=>13500-9500 = 1.8X-X = 0.8X

=>4000 = 0.8X

=>X = rs 5000/-

from eqn 1

r = (1500/5000)-0.2 = 0.1 =10/100

=>r = 10%

So sum of money is Rs 5000/- and rate of interest is 10%