the digits of a two digit number differ by 5. if the digits are interchanged and resulting number is added to the orignal , we get 99.
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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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