The digits of a two digit number differ by 5. On interchanging the digits, the number obtained exceeds the two original number by 27. Find the original as well as the new number.

  • matematika

    Subject:

    Math

  • Author:

    calvin

  • Created:

    1 year ago

Answers 1

Let the digit in ten's. Place be x and the digit in the one's place be y.

∴x−y=5⟶(i)

∴ Two digit number=10x+y

Two digit after reversing the digits=10y+x

According to question ,

∴10x+y+10y+x=99

⇒11x+11y=99

⇒x+y=9⟶(ii)

On adding (i) and (ii),

2x=14

⇒x=7

Putting the value of x in equation (i)

x−y=5

⇒y=2

∴ Number=10x+y

=72.

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