Question

sum of the digits of a two-digit number is 9 . the number obtained by interchanging the digits exceeds the given number by 27 . find the number

Answer 1

Hey!!!!

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let the ten's digit be x and unit digit be y

Then

=> x + y = 9

=> x = 9 - y --------(1)

Also

=> 10x + y + 27 = 10y + x

=> 9x - 9y = -27

=> x - y = -3

Using (1) in above equation

=> 9 - y - y = -3

=> -2y = -12

=> y = 6

Thus x = 9 - 6

=> x = 3

Thus Original Number = 30 + 6

=> 36

Thus the number is 36

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Hope this helps ✌️

Answer 2

Answer:36

Step-by-step explanation:

Let the perimeter be X

then tens digit is 9 - X

Number formed = 10(9-x)+x

when the digits are interchanged,

ones digit = 9-x

tens digit = x

Number formed = 10x+9-x

= 9x+9

According to question

new number - given number =27

=9x+9-(90-9x) = 27

=9x+9-90+9x = 27

= 18x=27+81

= 18x=108

= X=108÷18

X=6

Hence,the required number is 90-9*6=90-54=36