Let the digit in unit’s place be ‘x’ and the digit in ten’s place be ‘y’.
|
Digit in
tens place |
Digit in units place |
Number |
Sum of the digits |
Original
number |
y |
x |
10y + x |
y + x |
| Number obtained by interchanging the digits |
x |
y |
10x + y |
x + y |
According to the first condition.
the sum of the digits in a two-digit number is 9
x + y = 9 …(i)
According to the second condition,
the number obtained by interchanging the digits
exceeds the original number by 27
∴ 10x + y = 10y + x + 27
∴ 10x – x + y – 10y = 27
∴ 9x – 9y = 27
Dividing both sides by 9
, x – y = 3 …….(ii)
Adding equations (i) and (ii),
∴ x = 6
Substituting x = 6 in equation (i)
, x + y = 9
∴ 6 + y = 9
∴ y = 9 – 6 = 3
∴ Original number = 10y + x = 10(3)+ 6
= 30 + 6 = 36
∴ The two digit number is 36.
