$A$ sum of money at compound interest amounts in two years to Rs. $2809,$ and in three years to Rs. $2977.54.$ Find the rate of interest and the original sum.

The difference between simple and compound interest compounded annually on a certain sum of money for $2$ years at $4 \%$ per annum is $Rs. 1$. The sum (in $Rs.$) is

Aditya invested a certain amount in two different schemes $A$ and $B$. Scheme $A$ offers $S.I.$ at $12$ $p.c.p.a.$ and scheme $B$ offers $C.I.$ at $10$ $p.c.p.a.$ The interest accrued on the amount invested in scheme $A$ in $2$ years was $Rs. 3600$ and the total amount invested was $Rs. 35000$. What was the interest accrued on the amount (in $Rs.$) invested in scheme $B$?

The difference between the simple interest on a certain sum at the rate of $10 \%$ per annum for $2$ years and compound interest which is compounded every $6$ months is ₹ $124.05$. What is the principal (in ₹)?

Find the ratio of $S.I.$ and $C.I.$ on a certain sum of money at $5 \%$ per annum for $2$ years.

Mr. Dua invested money in two schemes $A$ and $B$ offering compound interest at $8 \%$ per annum and $9 \%$ per annum respectively. If the total amount of interest accrued through two schemes together in two years was ₹ $4818.30$ and the total amount invested was ₹ $27000$. What was the amount (in ₹) invested in scheme $A$?