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

Step-by-step explanation:

let unit digit be x and tens digit be y

than sum of digit = x+y

and number = x +10y

number obtained by interchange the digit = 10x +y

A/Q

x+y=9 (x= 9-y )☻

x +10y=10x+y+27

x-10x+10y-y=27

-9x+9y=27

-9(9- y)+9y=27

-81 +9y +9y =27

-81+18y=27

18y=27+81

18y= 108

y= 108/18

y=6..

x= 9 - y

=9-6

=3

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