## sum of the digits of a two digit number is 9 when when we interchange the digits it is found that the resulting new number is greater than t

Question

sum of the digits of a two digit number is 9 when 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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1 month 2021-08-21T13:30:14+00:00 2 Answers 0 views 0

The sum of the two digits is 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 be 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 is 6

Digit in tens place is 9-x= 9-6=3

Hence the number is 36

The required two digit number is 36

Step-by-step explanation:

Let the unit digit be y and tens digit be x

So the Number = 10x + y

Now the Reverse number obtained interchanging the digits = 10y + x

Now by the given condition

x + y = 9 …………………………(1)

And

10y + x = 10x + y + 27 …………………….(2)

9y – 9x = 27

9y – 9x = 27y – x = 3 ……………………………………..(3)

Adding Equation (1)and Equation (3) we get

2y =12

y = 6

So x =9 6 = 3

Hence Original Number = 36