If $A: B = 8: 15$,$B: C = 5: 8$,and $C: D = 4: 5$,then $A: D$ is equal to:

Three brothers divided ₹ $1620$ among themselves in such a way that the share of the second brother is equal to $\frac{5}{13}$ of the share of the other two combined. What is the share of the second brother?

In a college,$150$ students of $MBA$ are enrolled. The ratio of boys to girls is $7:8$. There are three disciplines in the college,namely,Marketing,$HR$,and Finance. In the Marketing discipline,there are $50\%$ girls of their total number and the boys are $40\%$ of their total number. In the $HR$ discipline,girls are $30\%$ of their total number while boys are $30\%$ of their total number. The Finance discipline has girls $20\%$ of their total number and the boys are $30\%$ of their total number. $7$ boys and $9$ girls are in the $HR$ and Marketing both. $6$ boys and $7$ girls are in the $HR$ and Finance both. $5$ boys and $8$ girls are in the Marketing and Finance both. $2$ boys and $3$ girls are enrolled in all the three disciplines. What percentage of students are enrolled in all three disciplines?

₹ $73,689$ are divided between $A$ and $B$ in the ratio $4:7$. What is the difference between thrice the share of $A$ and twice the share of $B$? (In ₹)

Three vessels having volumes in the ratio of $2: 3: 5$ are full of a mixture of water and milk. In the first vessel,the ratio of water and milk is $1: 3$,in the second $2: 3$,and in the third vessel,$2: 5$. If all the three vessels are poured into a large container,what is the resulting ratio of milk and water?

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: