Find the mean proportional between $9$ and $64$.

$A, B, C$ and $D$ share a property worth $₹ 77500$. If $A:B = 3:2$,$B:C = 5:4$ and $C:D = 3:7$,find the share of $B$ (in $₹$).

In two alloys,gold and silver are in the ratios of $4:1$ and $1:3$. After alloying together $10 \text{ kg}$ of the first alloy,$16 \text{ kg}$ of the second,and several kilograms of pure gold,an alloy was obtained in which the ratio of gold to silver was $3:2$. Find the weight of the new alloy (in $\text{kg}$).

The ratio of incomes of $P$ and $Q$ is $3:4$ and the ratio of their expenditures is $2:3$. If at the end of the year,each saves ₹ $2000$,then the income of $P$ is (in ₹):

An amount of ₹ $1200$ is distributed among $A, B$ and $C$ in the ratio of $5: 7: 13$. What is the difference between the shares (in ₹) of $C$ and $B$?

If $A: B = 2: 3$ and $B: C = 3: 7,$ then $A + B : B + C : C + A$ is