The price of a diamond is directly proportional to the square of its weight. $A$ man accidentally broke the diamond into three pieces in the ratio of $3:5:7$ and thus lost ₹ $42600$. What was the original price (in ₹) of the diamond?

The incomes of Gupta and Verma are in the ratio $9: 4$ and their expenditures are in the ratio $7: 3$. If each saves ₹ $2000$,then Gupta's expenditure is (in ₹):

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?

If two-third of $A$ is four-fifth of $B ,$ then $A : B =?$

If $A: B = 2: 3$ and $B: C = 3: 7,$ then $A + B : B + C : C + A$ is

The fourth proportional to $5, 8, 15$ is