Question

Please explain step by step.This question is taken from NCERT book.Please reply as soon as possible.

Sum of the digits of a two-digit is 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?

Thanks,
Ashok

Answer 1

Let the two digit number be xy.

The number can be written as 10x+y

If it is reversed, the number is 10y+x

As per the first condition,

x + y = 9

x + y - 9 = 0 ==> 1

As per second condition,

10y + x = 10x + y + 27

10x - x + y - 10y + 27 = 0

9x - 9y + 27 = 0

Divided by 9 ==> x - y + 3 = 0 ==> 2

By solving 1 and 2,

x = 3 and y = 6

So, the resulting two digit number is 36.

Thankyou