Question

sum of the digits of a two number is 9 when we interchange the digits, it is found that the resulting new number is greater that the original number by 27 what is the two digits number​

Answer 1

Answer:

Thus, x = 3. Therefore, the original number is 36.

Answer 2

Given :-

Sum  of the digits of a two number is 9 when we interchange the digits, it is found that the resulting new number is greater that the original number by 27

To Find :-

Number

Solution :-

Let

Unit digit = y

Tens digit = x

Number = 10x + y

x + y = 9 (1) (Given)

When we interchange the digits, it is found that the resulting new number is greater that the original number by 27

So,

10x + y = 10y + x + 27

10x - x = 10y - y + 27

9x = 9y + 27

9x - 9y = 27

Dividing both sides by 9

9x/9 - 9y/9 = 27/9

x - y = 3 (2)

On adding Eq. 1 and 2

x + y + x - y = 9 + 3

2x = 12

x = 12/2

x = 6

From 1

x + y = 9

6 + y = 9

y = 9 - 6

y = 3

Number = 10(3) + 6

Number = 30 + 6

Number = 36