Question

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?

Answer 1

let 1 digit be x
then another digit is 9-x
original no. = 10x+ 9-x
= 9+9x
when interchanged
new no. = 90-10x + x
90-9x
the new no. is greater than the original no. by27
=>90-9x=9+9x+ 27
=>90-9-27=18x
=>54=18x
=>54/18=x
x= 3
so the no. is 9+9*3
I. e. 36

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