The sides of a triangle are in the ratio $\frac{1}{2}: \frac{1}{3}: \frac{1}{4}$ and its perimeter is $104 \, cm$. The length of the longest side (in $cm$) is:

The ratio of the number of boys to girls in an institution is $6:5$. If there are $192$ boys in total,find the total number of students in the institution.

The ratio of incomes of $P$ and $Q$ is $3:4$ and the ratio of their expenditures is $2:3$. If at the end of the year,each saves ₹ $2000$,then the income of $P$ is (in ₹):

If $P: Q = 8: 15$,$Q: R = 5: 8$,and $R: S = 4: 5$,then $P: S$ is equal to

The sides of a triangle are in the ratio $1/2 : 1/3 : 1/4$ and its perimeter is $156 \text{ cm}$. The length of the largest side is (in $\text{cm}$):

$A$ mixture of milk and water is kept in two separate containers. The ratio of milk to water in one container is $5:1$ and in the other container is $7:2$. In what ratio should the mixtures from these two containers be mixed so that the quantity of milk in the new mixture becomes $80\%$?