If $A : B = 7 : 9$ and $B : C = 8 : 11,$ find $A : B : C$.

What will be the duplicate ratio of $2: 7$?

If $A: B = 2: 3$ and $B: C = 3: 7,$ then $A + B : B + C : C + A$ is

Find the fraction which bears the same ratio to $\frac{1}{27}$ that $\frac{3}{7}$ does to $\frac{5}{9}$.

If $4 \, \text{years}$ ago the ratio between the ages of $P$ and $Q$ was $5:6$ and the sum of their ages at present is $52 \, \text{years}$, what is the ratio of their present ages?

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.