Question

sum of the digits of a two-digit number is 9 then 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

hye

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let the 2 digit number be xy 

Assume the digit in ones place as x and the digit in tens place is y


The original number is (10y + x)


Number obtained by reversing the digits = (10x + y)


Now check for the condition


Given that sum of digits of the number is 9


That is x + y = 9   (1)


Second condition is, number obtained by interchanging the digits is greater
 than the original number by 27


That is (10x + y) = (10y + x) 27

⇒ 10x + y – 10y – x = 27

⇒ 9x – 9y  = 27

∴ x – y = 3  (2)

Add (1) and (2), we get

x + y = 9

x – y = 3

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2x = 12
∴ x = 6
Put x = 6 in (1), we get

6 + y = 9

⇒ y = 9 – 6 = 3

The original number = 10y + x = 10(3) + 6 = 36

=> 36
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hope it helps