Question

Sum of the digits of a two-digit number is 9. When we interchange that digit , 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 the 2 digits at ten's place be x and at one's palce be y.

then the original no. will be 10x+y

and x+y = 9 .........(i)

the no. obtained by interchanging the digits will be 10y+x


ATQ, (10y+x) - (10x+y) =27
10y+x - 10x -y = 27
9y-9x= 27
-x + y = 3............(ii)

by adding (i) and (ii) , we get-
y= 6

and putting this value in (i), we get,

x=3


Therefore, the original no. is= 10×3 +6= 36


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Answer 2

Answer:

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Given

The sum of the two digits = 9

On interchanging the digits, the resulting new number is greater than the original number by 27.

Let us assume the digit of units place = x

Then the digit of tens place will be = (9 – x)

Thus the two-digit number is 10(9 – x) + x

Let us reverse the digit

the number becomes 10x + (9 – x)

As per the given condition

10x + (9 – x) = 10(9 – x) + x + 27

⇒ 9x + 9 = 90 – 10x + x + 27

⇒ 9x + 9 = 117 – 9x

On rearranging the terms we get,

⇒ 18x = 108

⇒ x = 6

So the digit in units place = 6

Digit in tens place is

⇒ 9 – x

⇒ 9 – 6

⇒ 3

Hence the number is 36