A sum of $Rs. 8448$ is to be divided between $X$ and $Y$ who are respectively $18$ and $19 \,yr$ old, in such a way that if their shares be invested at $6.25 \%$ per annum at compound interest, they will receive equal amounts on attaining the age of $21 \,yr$. The present share of $X$ is (In $Rs.$)

A sum of money at compound interest amounts to thrice itself in $3$ years. In how many years will it be $9$ times itself?

At what rate per cent compound interest does a sum of money become $16$ times in $4$ years?

If the compound interest on a certain sum of money for $2$ years is $Rs. 164$ whereas the simple interest for $3$ years at the same rate is $Rs. 240$ on the same sum, find the sum (In $Rs.$)

A tree increases annually by $\frac{1}{8}$ of its height. By how much will it increase (In $cm$) after $2$ years, if it stands today $64 cm$ high?