What should be subtracted from each term of the ratio $19: 23$ to make it equal to the ratio $3: 4$?

If $\frac{5a+3b}{2a-3b} = \frac{23}{5}$,then the value of $a:b$ is:

Three numbers are in the ratio $5:6:7$. If the product of the numbers is $5670$,then the greatest number is:

In a college, $150$ students of $MBA$ are enrolled. The ratio of boys to girls is $7:8$. There are three disciplines: Marketing, $HR$, and Finance. In Marketing, $50\%$ of the girls and $40\%$ of the boys are enrolled. In $HR$, $30\%$ of the girls and $30\%$ of the boys are enrolled. In Finance, $20\%$ of the girls and $30\%$ of the boys are enrolled. $7$ 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 in all three disciplines. Find the ratio of the number of boys in both Marketing and Finance to the number of girls only in Finance.

Two numbers are such that the ratio between them is $4:7$. If each is increased by $4$,the ratio becomes $3:5$. The larger number is:

An amount of money is to be distributed among $P, Q$ and $R$ in the ratio of $2: 7: 9$. The total of $P$'s and $Q$'s share is equal to $R$'s share. What is the difference between the shares of $P$ and $Q$?