Question

A number when divided successively by $4$ and $5$ leaves remainders $1$ and $4$ respectively, when it is successively divided by $5$ and $4$, then the respective remainders will be

• A. $1,2$
• B. $2,3$
• C. $3,2$
• D. $4,1$

Answer 1

The correct option is B $2,3$

Let the number be $X$.
When you divide $X$ by $4$ it gives remainder $1$.

Let the dividend here be $Y$
$\Rightarrow X=4Y+1$ ...(1)
Now, when we divide $Y$ by $5$, we get remainder $4$.

We take quotient as $1$, as $5$ divided $Y$ completely.
$\Rightarrow Y=1\times 5+4=9$
Putting $Y=9$ in eqn (1), we get
$X=4\times 9+1=37$
Now, $37$ divide by $5$ and $4$ respective it will gives $2$ and $3$.

Hence, option B.