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Question

Sum of digits of a two digit number is 9.If 27 is added to the number,the digits of the original number get interchanged.Find the original number.

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Solution

Let the number be xy [that is x in 10th place and y in once place]
So no. value can calculated as 10x+y

When digits are interchanged ,value of no =10y+x
x+y=9...............(1)
Given as
(10x+y)+27=10y+x


10x-x+y-10y=-27
9x-9y=-27
x-y=-3................(2)
add equation 1 and 2
we get
x=3
substitute it in eq 1
y=6
so the number is 36

when we reverse ,the no =63

and 36+27 =63

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