Question

The sum of the digit of a two-digit number is 9. The number got by interchanging the digit is 27 more than the original number. What is the number.
​

Answer 1

Let the

number in ten's place be x

one's place be y

Number obtained → 10x + y

Also,

The sum of digits of 2 digit number is 9

⇒ x + y = 9 → (Equation 1)

The number obtained by interchanging it's digits exceeds the original number by 27

⇒ (10y + x) = (10x + y) + 27

⇒ (10y + x) - (10x + y) = 27

⇒ 10y + x - 10x - y = 27

⇒ 9y - 9x = 27

⇒ 9(y - x) = 9(3)

Dividing by 9 on both sides,

y - x = 3 → (Equation 2)

Adding Equation 1 and 2;

x + y = 9

(+) - x + y = 3

2y = 12

⇒ y = 6

Now, Substitute value of y in any one of the equation

Here we have Substituted in Equation 1

x + y = 9

x + 6 = 9

x = 9 - 6

x = 3

∴ The number is (10x + y)

= 10(3) + 6

= 36