Question

The sum of the digits of a two-digit number is 11. If the digits of the number are interchanged, we get a number which 27 more than the original number. What is the number?

Answer 1

Let the digits at tens and units place of a two-digit number be x and y respectively.

Sum of the digits of the two-digit number = 11

⇒ x + y = 11 … (1)

We know that any two digit number is represented by 10x + y.

If the digits are interchanged then the two-digit number is represented by 10y + x.

According to the question:

10y + x = 10x + y + 27

⇒ 10y + x − 10x − y = 27

⇒ 9y − 9x = 27

⇒ y − x = 3 ... (2)

Adding equation (1) and (2):

2y = 14

⇒ y =

⇒ y = 7

From equation (1), we get:

x = 11 − 7 = 4

Number = 10x + y = 40 + 7 = 47

Thus, the two digit number is 47.