Two numbers are in the ratio $1: 2$. If $7$ is added to both,the ratio changes to $3: 5$. The greatest number is:

Three numbers $A, B$ and $C$ are in the ratio $12: 15: 25$. If the sum of these numbers is $364$,find the ratio between the difference of $B$ and $A$ and the difference of $C$ and $B$.

Three numbers are in the ratio $2:3:4$. If the sum of their squares is $1856$,then the numbers are:

The ratio of the ages of a man and his wife is $4:3$. After $4$ years,this ratio will be $9:7$. If at the time of marriage,the ratio was $5:3$,then how many years ago were they married?

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 $\text{kg}$).

An office opens at $10 \, AM$ and closes at $5 \, PM$. The lunch interval is for $30$ minutes. The ratio of the lunch interval to the total office hours is: