The sum of the digits of a two digit number is 9 .if 27 is added to it ,the digits of the numbers get reversed . The number is
Answers
Given: The sum of the digits of a two digit number is 9. If 27 is added to it ,the digits of the numbers get reversed.
To find: The number
Solution: Let the digits of the two digit number be a and b where a is tens digit and b is ones digit.
Since the sum of digits is 9, therefore the equation can be written as:
a+b= 9 -------(i)
The value of any number whose tens and ones digit are known can be written as
= 10( tens digit) + ones digit
= 10a + b
On reversing the number, a becomes the one digit and b becomes the tens digit.
Therefore, the number can be written as
= 10b+a
Now, the number is reversed when 27 is added to it. Therefore,
10a+b +27 = 10b+a
=> 10a-a + b-10b = -27
=> 9a - 9b = -27
=> 9(a-b) = -27
=> a-b = -27/9
=> a-b = -3--------(ii)
Adding (i) and (ii),
a +b + a - b = 9-3
=> 2a = 6
=> a = 6/2
=> a = 3
Using a = 3 in equation (ii),
3-b= -3
=> -b = -3-3
=> -b = -6
=> b = 6
Therefore, the number
= 10a+b
= 10(3) + 6
= 30+6
= 36
On adding 27 to 36, the sum comes out to be 63 which is the number that we get on reversing the digits of 36.
Therefore, the number is 36.