sum of digits of a two-digit number is 9 then we interchange the digits it is found that the resulting new number is greater than original number by 27 what is the two digit number?
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Let the digits at tens place and ones place: x and 9−x respectively.
∴ original number =10x+(9−x)
=9x+9
Now Interchange the digits: Digit at ones place and tens place: x and 9−x respectively.
∴ New number: 10(9−x)+x
=90−10x+x
=90−9x
AS per the question
New number = Original number +27
90−9x=9x+9+27
90−9x=9x+36
18x=54
x=
18
54
x=3
Digit at tens place ⇒3 and one's place : 6
∴ Two digit number: 36
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