$A$ mixture contains alcohol and water in the ratio $4:3$. If $5 \text{ liters}$ of water is added to the mixture,the ratio becomes $4:5$. Find the quantity of alcohol in the given mixture (in $\text{L}$).

When $X$ is subtracted from the numbers $9, 15$ and $27$,the remainders are in continued proportion. What is the value of $X$?

The students in three classes are in the ratio $4:6:9$. If $12$ students are increased in each class,the ratio changes to $7:9:12$. Then the total number of students in the three classes before the increase is

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 boys and girls in a school is $9:5$. If the total number of students in the school is $1050$,then the number of boys is