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?
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Answer 1

Answer:

$\huge\frak\red{Answer}$

36

$\huge\frak\red{explanation}$

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

Answer 2

Answer:

Step-by-step explanation:

let the digits be x and y

now, x+y=9

original no. = 10x + y

new no. = 10y + x = 10x + y + 27

solving the equation, 9y = 9x + 27

                                    9y = 9(x+ 3)

                                      y= x+3

now x+y = 9

so x + (x+3) = 9

    x=3

and y= 6

original no. = 36

new no. formed = 63