Two numbers are in the ratio $3:5$. If $9$ is subtracted from each,they are in the ratio $12:23$. Find the smaller number.

Present ages of $X$ and $Y$ are in the ratio $5: 6$ respectively. Seven years hence,this ratio will become $6: 7$ respectively. What is $X$'s present age in years?

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 $50\%$ of the total girls and $40\%$ of the total boys. In the $HR$ discipline,there are $30\%$ of the total girls and $30\%$ of the total boys. In the Finance discipline,there are $20\%$ of the total girls and $30\%$ of the total boys. $7$ boys and $9$ girls are in both $HR$ and Marketing. $6$ boys and $7$ girls are in both $HR$ and Finance. $5$ boys and $8$ girls are in both Marketing and Finance. $2$ boys and $3$ girls are enrolled in all three disciplines. What is the ratio of boys to girls only in the Marketing discipline?

If ₹ $126.50$ is divided among $A, B$ and $C$ in the ratio of $2: 5: 4$,the share of $B$ exceeds that of $A$ by (in ₹) (in $.50$)?

The ratio of the number of boys to girls in an institution is $6:5$. If there are $192$ boys in total,find the total number of students in the institution.

If $78$ is divided into three parts which are in the ratio of $1: \frac{1}{3}: \frac{1}{6},$ the middle part is