Three numbers are in the ratio $2:3:4$. If the sum of their squares is $1856$,then the numbers are:

The mean proportional between $64$ and $81$ is

In a mixture of petrol and kerosene,the quantity of petrol is $99 \text{ litres}$. If this same quantity of petrol were present in another mixture of petrol and kerosene where the total volume is $198 \text{ litres}$ less than the actual mixture,the concentration of petrol in the actual mixture would be $13.33 \%$ less than that of the new mixture. What is the concentration (in $\%$) of petrol in the actual mixture?

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

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. The ratio of boys to girls enrolled only in the $HR$ discipline is:

The number that must be added to each of the numbers $8, 21, 13$ and $31$ to make the ratio of the first two numbers equal to the ratio of the last two numbers is: