Two numbers are in the ratio of $5: 8$. If $12$ is added to each,they are in the ratio of $3: 4$. Find the sum of the two numbers.

The sum of two numbers is $25$ and their difference is $7 \frac{1}{2}$. Find the ratio of the numbers.

The value of $k$ that must be added to $7, 16, 43,$ and $79$ so that they are in proportion is

The prices of a scooter and a television set are in the ratio of $3:2$. If a scooter costs ₹ $600$ more than the television set,then the price of the television set is (in ₹):

₹ $600$ is divided among $A, B$ and $C$. If $\frac{2}{5}$ of $A$'s share plus ₹ $40$,$\frac{2}{7}$ of $B$'s share plus ₹ $20$,and $\frac{9}{17}$ of $C$'s share plus ₹ $10$ are all equal,then what is $A$'s share 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: 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?