The logical 9 by Satyabrata Dash

This question is one of the famous and recurring question. Wrote the P, Q, R, S into $9(1000s+100r+10q+p)=1000p+100q+10r+s$ Provided that $0 \leq p, q, r, s \leq 9$ , the expansion provides us instantly that $s = 1$ and $p = 9$ . Upon putting this two value in, it gives $9(1009+100r+10q) = 9001+100q+10r$ or simply $8+89r = q$ With the conditions provided, we can conclude that $r = 0$ and $q = 8$ , hence $\overline{pqrs} = 9801$