The value of a machine depreciates at the rate of $12\%$ per annum. It was purchased $3$ years ago. Its present value is $Rs. 29644.032$. What was the purchase price (in $Rs.$) of the machine?

The difference between simple and compound interest on a sum of $10000$ is $64$ for $2$ years. Find the rate of interest. (in $\%$)

Find the difference between $S.I.$ and $C.I.$ (in $Rs.$) at $14 \%$ per annum for $2$ years on a principal of $Rs. 10000$.

Raghu invested a certain sum in Scheme $X$ for $4$ years. Scheme $X$ offers simple interest at $12\%$ per annum for the first two years and compound interest (compounded annually) at $20\%$ per annum for the next two years. The total interest earned by him after $4$ years is $₹ 11016$. What was the sum (in $₹$) invested by Raghu in Scheme $X$?

What would be the $C.I.$ obtained on an amount of $Rs. 12000$ at the rate of $9 \,p.c.p.a$ for $3$ years (in $Rs.$)?

Divide $Rs. 2602$ between $X$ and $Y$,so that the amount of $X$ after $7 \,yr$ is equal to the amount of $Y$ after $9 \,yr$,the interest being compounded at $4 \%$ per annum.