The solution of the pair of equations $x + 2y = 5$ and $3x + 5y = 13$ is ...........

The sum of the digits of a two-digit number is $13$. The number obtained by interchanging the digits is $9$ more than the original number. Find the original number.

$A$ fraction becomes $\frac{1}{4}$ if $2$ is subtracted from the numerator and $3$ is added to the denominator. If $6$ is added to the numerator and the denominator is multiplied by $3$,it becomes $\frac{2}{3}$. Find the fraction.

Vijay had some bananas,and he divided them into two lots $A$ and $B$. He sold the first lot at the rate of $Rs. 2$ for $3$ bananas and the second lot at the rate of $Rs. 1$ per banana,and got a total of $Rs. 400$. If he had sold the first lot at the rate of $Rs. 1$ per banana,and the second lot at the rate of $Rs. 4$ for $5$ bananas,his total collection would have been $Rs. 460$. Find the total number of bananas he had.

The sum of the present age of a father and twice the present age of a son is $70$ years. Also,the sum of twice the present age of father and the present age of son is $95$ years. Find their present ages.

Solve the following pair of equations: $(a \neq 0, b \neq 0)$
$\frac{2}{a} + \frac{3}{b} = 1$
$\frac{1}{a} + \frac{1}{b} = 1$