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Question

The digits of two - digits number is differ by 5 . If the digits are interchanged and the resulting number is added to the original number , we get 99 . Find the original number .

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Solution

Let the digit in ten's. Place be x and the digit in the one's place be y.
xy=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)
xy=5
y=2
Number=10x+y
=72.

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