the compound interest on certain sum for the third year and fourth year is rs.1815 and rs 1996.50 respectively. what is the annual rate of interest

Answer 1

x(1+r)^3 = x + 1815 **
x(1+r)^4 = x + 1996.5 ***
divide *** by **

1+r = (x+1996.5)/(x+1815)
x + 1815 + rx + 1815r = x + 1996.5
rx + 1815r = 181.5
r(x + 1815) = 181.5
r = 181.5/(x+1815)

so it looks like it depends on the value of x
if x = 10000
r = 181.5/11815 = .01536

if x = 5000
r = 181.5/.0266

etc

I followed the wording of your question.
Did you mean,
"The compound interest amount on a certain sum ...."
then it would change the question entirely and we could sy
x(1+r)^3 = 1815
x(1+r)^4 = 1996.5
now divide them:
1+r = 1.1
r = 0.1 or 10%

Answer 2

Amount = $ 21952 , CI = $ 6327