An office opens at $10 \, AM$ and closes at $5 \, PM$. The lunch interval is for $30$ minutes. The ratio of the lunch interval to the total office hours is:

Calculate the fourth proportional to the numbers $286, 78, 1342$.

What is the fourth proportional to $189, 273$ and $153$?

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:

When $x$ is added to each term of $7: 13$,the ratio becomes $2: 3$. The value of $x$ is

$A$ 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 $\text{L}$).