$A$ fraction is greater than twice its reciprocal by $\frac{7}{15}$. What is the fraction?

$A$ and $B$ are positive integers. If $A + B + AB = 65$,then what is the difference between $A$ and $B$ (given $A, B \leq 15$)?

The greatest number among $3^{50}, 4^{40}, 5^{30}$ and $6^{20}$ is

The sum of two numbers is $100$ and their difference is $37$. The difference of their squares is

Natu and Buchku each have a certain number of oranges. Natu says to Buchku,"If you give me $10$ of your oranges,$I$ will have twice the number of oranges left with you." Buchku replies,"If you give me $10$ of your oranges,$I$ will have the same number of oranges as left with you." What is the number of oranges with Natu and Buchku respectively?

Find the nearest number to $12199$ which is exactly divisible by the product of the first four prime numbers.