Question

3. Sum of the digits of a two-digit number is 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?
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Answer 1

Answer:

Assumption:-

Let the tens digit be x and unit digit be y

Number formed(Orignal number)=10x+y

Number formed by reversing the digits(new number)=10y+x

According to question:-

x+y=9 (1)

Orignal number+27=new number

10x+y+27=10y+x

10x-x+y-10y= -27

9x-9y= -27

By elimination method:-

x+y= 9 (1)×9

9x-9y= -27 (2)

9x+9y=81 (1)

9x-9y= -27 (2) Subtracting eq(2) from eq(1)

(-) (+) (+)

18y=108

y=108/18

y=6

Substituting y=6 in (1)

x+y=9

x+6=9

x=9-6

x=3

Hence:-

Orignal number=10x+y

=10(3)+6

=30+6

=36

Verification:-

Orignal number+27=new number

10x+y+27=10y+x

36+27=10(6)+3

63=60+3

63=63

Since,

LHS=RHS

Hence,

Orignal number=36