Question

2. The sum of the digits of a two-digit number is 17. If the number formed by reversing the digits is less
than the original number by 9, find the original number.
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Answer 1

Answer:

Let the unit's place=x

Then the ten's place=15−x

∴ original number=10(15−x)+x=150−10x+x=150−9x

By reversing the digits, we get

New number=10x+(15−x)=10x+15−x=9x−15

According to the problem,

original number−New number=27

⇒150−9x−9x+15=27

⇒−18x+165=27

⇒−18x=27−165=−108

⇒x=

−18

−108

=6

Hence original number=150−9x=150−9×6=150−54=96