Question

the sum of the digits of a two digit number 9 . when we interchange the digits, it is found that the resulting new number is greater than the original number by 27 . what is the two digit number.

Answer 1

Let’s say x is the unit digit and y is the tenth digit.

y+x = 9 -> y=9-x

10x+y = 10y+x+27

10x+9-x = 10(9-x)+x+27

10x+9-x = 90–10x+x+27

18x = 108

x = 6

so y = 3

let’s check

63 - 39 =27

27 = 27 (correct)

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Answer 2

let the unit digit =x
Two digit number=9-x

sum of digit of the two digit no. is 9
original no. =10(9-x) +x
=90-10x+x
=90-9x

when we interchange the digit
unit digit= 9-x
Ten's digit=x

Resulting no. =10x+(9-x)
=9x+9

According to the q.
=(9x+9) = (90-9x) +27
=9x+9x=90+27-9
=18x =108
=1x=108/18 =6


9-x=9-6=3

hence the required two digit number is 36 ...


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