The population of a state increases by $10 \%$ every year. If its population in the year $2003$ was $15$ lakhs,what was its population in the year $2005$ (in lakhs)?

$A$ certain sum will amount to ₹ $12,100$ in $2$ years at $10 \%$ per annum of compound interest,interest being compounded annually. The sum is (In ₹)

$A$ man borrows ₹ $3825$ to be paid back with compound interest at the rate of $4 \%$ per annum by the end of $2$ years in two equal yearly instalments. How much will be each instalment (in ₹)?

$B$ borrows ₹ $5,000$ from $A$ at $6 \%$ p.a. simple interest and lends it to $C$ at compound interest of $10 \%$ p.a. If $B$ collects the money back from $C$ after $2$ years and repays $A$,the profit made by $B$ in the transaction is (in ₹):

$A$ sum of money amounts to ₹ $6655$ at the rate of $10 \%$ compounded annually for $3$ years. The sum of money is (in ₹):

If the difference between the $C.I.$ compounded half-yearly and simple interest on a sum at $10 \%$ per annum for one year is $Rs. 25$,the sum (in $Rs.$) is: