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

The salaries of $A, B, C$ 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?

Two numbers are in the ratio of $5: 7$. If $25$ is subtracted from each,they are in the ratio of $35: 59$. Find the difference of the two 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 $50\%$ girls of their total number and the boys are $40\%$ of their total number. In the $HR$ discipline,girls are $30\%$ of their total number while boys are $30\%$ of their total number. The Finance discipline has girls $20\%$ of their total number and the boys are $30\%$ of their total number. $7$ boys and $9$ girls are in $HR$ and Marketing both. $6$ boys and $7$ girls are in $HR$ and Finance both. $5$ boys and $8$ girls are in Marketing and Finance both. $2$ boys and $3$ girls are enrolled in all the three disciplines. By what percent is the number of boys in the Marketing discipline more than the number of girls in the $HR$ discipline?

Annual incomes of Amit and Varun are in the ratio $3:2,$ while the ratio of their expenditures is $5:3.$ If at the end of the year each saves $Rs. 1000,$ the annual income of Amit is (in $Rs.$):

$A$ person distributes his pens among four friends $A, B, C$ and $D$ in the ratio $\frac{1}{3}: \frac{1}{4}: \frac{1}{5}: \frac{1}{6}$. What is the minimum number of pens that the person should have?