Question

$24P$ leaves remainder $1$ if it is divided by $3$ and leaves remainder $2$ if it is divided by $5$.

Find the value of $P$

Answer 1

As $24P$ is a number, then $P$ must be a unit digit.
(i) Since, on dividing by $3$ remainder is $1$.
This implies that $P$ can be $4,7$ as $\frac{240+P}{3}=80+\frac{P}{3}$ and $\frac{P}{3}$ gives $1$ as remainder. Hence, $P=4$ or $7$
(ii) Now, on dividing by $5$ remainder is $2$.
This implies that $P$ must be $7$ as $\frac{240+P}{5}=48+\frac{P}{5}$ and $\frac{P}{5}$ gives $2$ as remainder. Hence, $P=7$
Both Conditions (i), (ii) implies $P=7$.
Therefore, answer is $P\to 7$