Find the third proportional to the numbers $4$ and $42$.

If $a-b : b-c : c-d = 1 : 2 : 3$,then what is the value of $(a+d) : c$?

If $A = \frac{4}{5}$ of $B$ and $B = \frac{5}{2}$ of $C$,then the ratio of $A : C$ 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: 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 $HR$ and Marketing both. $6$ boys and $7$ girls are in $HR$ and Finance both. $5$ boys and $8$ girls are in Marketing and Finance both. $2$ boys and $3$ girls are enrolled in all the three disciplines. By what percent is the number of boys in the Marketing discipline more than the number of girls in the $HR$ discipline?

If $Rs. 782$ is divided into three parts proportional to $\frac{1}{2}: \frac{2}{3}: \frac{3}{4}$,then the first part is (in $Rs.$):

What should be subtracted from $15, 28, 20,$ and $38$ so that the remaining numbers are in proportion?