Question

a number consists of two digits, of which the ten's digit exceeds the unit's digit by 6. If the number itself is equal to ten times the sum of the digits, then the number is ____​

Answer 1

Answer:

Subtracting 18 from a number that is two digits ab in decimal such that a=b+2 will always reverse its digits because:

10a+b−18=10(b+2)+b−18=10b+(b+2)=10b+a

Hence you can choose any digits satisfying a=b+2 . For example b=2 gives 42−18=24 .

This works even for non-traditional "digits" such as a=10 (which is 108−18=90 in traditional notation) or b=−1 (which is 9−18=−9 in traditional notation). For example b=42 gives 482−18=464 (forty-two tens plus forty-four ones) ⌣¨