Find the sub-duplicate ratio of $81: 64$.

Three vessels having volumes in the ratio of $2: 3: 5$ are full of a mixture of water and milk. In the first vessel,the ratio of water and milk is $1: 3$,in the second $2: 3$,and in the third vessel,$2: 5$. If all the three vessels are poured into a large container,what is the resulting ratio of milk and water?

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

In a college,$150$ students of $MBA$ are enrolled. The ratio of boys to girls is $7:8$. There are three disciplines in the college: Marketing,$HR$,and Finance. In the Marketing discipline,there are $50\%$ of the total girls and $40\%$ of the total boys. In the $HR$ discipline,there are $30\%$ of the total girls and $30\%$ of the total boys. In the Finance discipline,there are $20\%$ of the total girls and $30\%$ of the total boys. $7$ boys and $9$ girls are in both $HR$ and Marketing. $6$ boys and $7$ girls are in both $HR$ and Finance. $5$ boys and $8$ girls are in both Marketing and Finance. $2$ boys and $3$ girls are enrolled in all three disciplines. What is the ratio of boys to girls only in the Marketing discipline?

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 the number of boys and girls in a school of $720$ students is $7: 5$. How many more girls should be admitted to make the ratio $1: 1$?