$P$ varies inversely with the product of $Q$ and $R$. When $Q = 6$ and $R = 12$,$P = 75$. When $Q = 5$ and $R = 10$,what is the value of $P$?

Find two numbers such that their mean proportion is $10$ and their third proportion is $1024$.

There are three sections $A, B$ and $C$ in a school of class $I$. The ratio of students in sections $A$ and $B$ is $3:5$ and that in $B$ and $C$ is $4:7$. If the total number of students in the class is $201$,then the number of students in section $A$ is:

If $33 \%$ of $A$ is equal to $55 \%$ of $B$,then find the ratio of $A$ and $B$.

The prices of a refrigerator and a television set are in the ratio $5:3$. If the refrigerator costs $Rs. 5500$ more than the television set,then the price of the refrigerator is (in $Rs.$):

Two numbers are in the ratio of $5: 7$. If $25$ is subtracted from each,they are in the ratio of $35: 59$. Find the difference of the two numbers.