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?

The sides of a triangle are in the ratio $\frac{1}{2}: \frac{1}{3}: \frac{1}{4}$ and its perimeter is $104 \, cm$. The length of the longest side (in $cm$) is:

An alloy of copper and zinc is taken in the ratio $1: 2$,and another alloy of the same metals is taken in the ratio of $2: 3$. How many parts of the two alloys must be taken to obtain a new alloy consisting of copper and zinc that are in the ratio $3: 5$?

The salaries of $A, B$ and $C$ are in the ratio $2: 3: 5$. If increments of $15\%, 10\%$ and $20\%$ are allowed respectively in their salaries,then what will be the new ratio of their salaries?

The sum of two numbers is $25$ and their difference is $7 \frac{1}{2}$. Find the ratio of the numbers.

Two candles of the same height are lighted at the same time. The first is consumed in $8 \text{ hours}$ and the second in $6 \text{ hours}$. Assuming that each candle burns at a constant rate,in how many hours after being lighted,the ratio between the height of the first and second candles becomes $2:1$?