₹ $11,550$ has to be divided between $X$,$Y$,and $Z$ such that $X$ gets $\frac{4}{5}$ of what $Y$ gets and $Y$ gets $\frac{2}{3}$ of what $Z$ gets. How much more does $Z$ get over $X$ (in ₹)?

If $6 A = 11 B = 7 C$,find $A : B : C$.

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 $\text{kg}$).

On Republic Day,sweets were to be equally distributed among $450$ children. But on that particular day,$150$ children remained absent. Thus,each child got $3$ sweets extra. How many sweets did each child get?

If $1,000$ copies of a book of $25$ sheets require $50$ reams of paper,how much paper is required for $5,000$ copies of a book of $32$ sheets?

If $Rs. 782$ is divided into three parts proportional to $\frac{1}{2}: \frac{2}{3}: \frac{3}{4}$,then the first part is (in $Rs.$):