Question

Find a two-digit number whose product of the digits is 8 and when 18 is added to this number, the digits are reversed.

Answer 1

Represent the digits by "AB". The number=10A+B.

AB=8; 10A+B+18=10B+A, 9(B-A)=18, B-A=2.

B=8/A so 8/A-A=2, 8-A²=2A, A²+2A-8=(A+4)(A-2)=0.

Since the digits are positive integers, A=2 and B=8/A=8/2=4.

The number is 24, 24+18=42 which is the number reversed.