Question

sum of digits of a two-digit number is 9 then we interchange the digits it is found that the resulting new number is greater than original number by 27 what is the two digit number

Answer 1

Let the two digits of the number be x and y where x is in the ten's place and y in the unit's place. So the number will be 10x + y and 10y + x is the number we get if we interchange the digits.

Eg: 45 = 10*4 + 5 and interchanging the digits we get 54 = 10*5 + 4

now, as per the given information in the question:

eqn 1) x + y = 9 and

eqn 2) 10x + y + 27 = 10y + x,

the above equation can be simplified to:

eqn 3) 9x - 9y = -27

Now solving for x and y using the two equations eqn1 and eqn3 we get:

x = 3 and y = 6

So, the two digit number is 10*3 + 6 = 36