Lời giải:
$\overline{a2bc}=\overline{abc}\times 9$
$1000\times a+200+10\times b+c=9\times (100\times a+10\times b+c)$
$1000\times a+200+10\times b+c=900\times a+90\times b+9\times c$
$100\times a+200=80\times b+8\times c$
$25\times a+50=20\times b+2\times c$
Có:
$25\times a=20\times b+2\times c-50< 20\times 10+2\times 10-50=170$
$\Rightarrow a< 6,8$
Mà:
$25\times a=20\times b+2\times c-50$ chẵn nên $a$ chẵn
$\Rightarrow a=2,4,6$
Nếu $a=2$ thì:
$20\times b+2\times c=100$
$10\times b+c=50$
$\Rightarrow \overline{bc}=50$
Số cần tìm là $250$
Nếu $a=4$ thì:
$20\times b+2\times c=150$
$10\times b+c=75$ hay $\overline{bc}=75$
Số cần tìm là $475$
Nếu $a=6$ thì:
$20\times b+2\times c=200$
$10\times b+c=100$ hay $\overline{bc}=100$ (vô lý - loại)
Vậy............