Question

In a math contest the teacher tells one of the participants that there is a three-digit number, and that if the unit digit and the tens digit are exchanged, the number is increased by 18, and if the digit of the tens and hundreds digit are exchanged, the number is decreased by 90. The sum of the digits is 12. What is the number the participant must find?

Please explain with process

Answer 1

Let, number is of the form 10+
10
a
+
b
, then according to question:

+=8
a
+
b
=
8
and digits of 10++9
10
a
+
b
+
9
are equal.

Notice that adding 9
9
to the give number will increase its tens digit by 1
1
and decrease its unit digit by 1
1
. So,

+1=−1⟹+2=
a
+
1
=
b
−
1
⟹
a
+
2
=
b
.

Hence, we have +2+=8⟹=3⟹=5⟹10+=35