The sum of the digits of a two digits number is 7 the number obtained by interchanging the digits exceeds the original number by 27 find the no.
Answers
Given:
The sum of the digits of a two digit number is 7.
The number obtained by interchanging the digits exceeds the original number by 27.
Find:
The numbers
Solution:
Let the digit at the unit's place be 'y'
Let the digit at ten's place be 'x'
NUMBER = 10x + y
The sum of the digits of a two digit number is 7.
=> x + y = 7
=> x = 7 - y .......(i).
The number obtained by interchanging the digits exceeds the original number by 27.
Number obtained by reversing the digits = 10y + x
Number obtained by reversing the digits = Original number + 27
=> 10y + x = 10x + y + 27
=> -27 = 10x - x + y - 10y
=> -27 = 9x - 9y
=> -27 = 9(x - y)
=> -27/9 = x - y
=> -3 = x - y ......(ii).
Putting the value of 'x' in equation (ii).
=> -3 = x - y
=> -3 = 7 - y - y
=> - 3 = 7 - 2y
=> -3 - 7 = -2y
=> -10 = -2y
=> -10/-2 = y
=> 5 = y
=> y = 5
Putting the value of 'y' in equation (i).
=> x = 7 - y
=> x = 7 - 5
=> x = 2
Now,
Number = 10x + y
=> 10(2)+5
=> 20+5
=> 25
Hence, the number is 25.
I hope it will help you.
Regards.
Number obtained by reversing the digits = Original number + 27
=> 10y + x = 10x + y + 27
=> -27 = 10x - x + y - 10y
=> -27 = 9x - 9y
=> -27 = 9(x - y)
=> -27/9 = x - y
=> -3 = x - y ......(ii).