Question

When a number is divided by $13$, the remainder is $11$, when the same number is divided by $17$, the remainder is $9$. What is the number ?

Answer 1

Let $c$ be the required number.
$x=13p+11$ and $$x = 17q + 9$
$13p+11=17q+9$
$17q-13p=2$
$q=\frac{(2+13p)}{17}$
Here, we can solve this question with normal process because there is two variable in it but one equation.

So, we will do it by putting different values of $p$.
The least value of $p$ for $q$ is a whole number is $26$.
$x=13\times 26+11=349$