Question

A number when divided by $259$, leaves a remainder $139$. What will be the remainder when the same number is divided by $37$?

Answer 1

Let the number be $P$.

So, $P-139$ is divisible by $259$.
Let $Q$ be the quotient, then
$\frac{P-139}{259}=Q$

$\Rightarrow P=259Q+139$
$\Rightarrow \frac{P}{37}=\frac{259Q+139}{37}$ ...$\because 259$ is divisible by $37$

$\Rightarrow \frac{P}{37}=7Q+3+\frac{28}{37}$
$\therefore$ When 139 is divided by $37$, it leaves a remainder of $28$.