If $a:b = \frac{2}{9} : \frac{1}{3}$,$b:c = \frac{2}{7} : \frac{5}{14}$,and $d:c = \frac{7}{10} : \frac{3}{5}$,then find $a:b:c:d$.

In a school,there were $1554$ students and the ratio of the number of boys to girls was $4:3$. After a few days,$30$ girls joined the school but some boys left; as a result,the ratio of boys to girls became $7:6$. The number of boys who left the school is:

The ratio of the incomes of $A, B$ and $C$ is $3: 7: 4$ and the ratio of their expenditures is $4: 3: 5$. If in the income of $Rs. 2400$, $A$ saves $Rs. 300$, then the savings of $B$ and $C$ respectively are:

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?

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.

Find the third proportional to the numbers $4$ and $42$.