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?

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?

$A$ 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 $80\%$?

$A$ and $B$ earn in the ratio $2:1$. They spend in the ratio $5:3$ and save in the ratio $4:1$. If the total monthly savings of both $A$ and $B$ are ₹ $5,000$,the monthly income of $B$ is (in ₹): (in $,000$)

If two numbers are in the ratio $2:3$ and the ratio becomes $3:4$ when $8$ is added to both the numbers,then the sum of the two numbers is

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 ₹):