Question

In a $3$-digit number, unit's digit is one more than the hundred's digit and ten's digit is one less than that hundred's digit. If the sum of the original $3$-digit number and numbers obtained by changing the order of digits cyclically is $2664$, find the number.

Answer 1

Let hundred digit $=x$

ten digit $=x-1$

unit digit $=x-1$

First form of Number $=100\times x+100(x-1)+x+1$

$=111x-9$

Second form of Number $=(x+1)100+x\times 10+x-1$

$=111x+99$

third form of number $=(x-1)100+(x+1)10+x$

$=111x-90$

So $111x-9+111x+99+111x-90=2664$

$111x=2664$

$x=8$

So the number $8\times 100+7\times 10+9$

$=879$