Question

The sum of digits of a two digit number is 8. If 18 is added to the number, its digits interchange. Find the number.

Answer 1

Given:

Sum of digits of a two-digit number is 8. If 18 is added to the number, its digits get interchanged. Find the number.

Step-wise calculation:

Let the two-digit number be (10x + y), where (x) is the tens digit and (y) is the units digit.

1. Sum of digits is 8:

x + y = 8   ...(1)

2. When 18 is added, the digits interchange:

10x + y + 18 = 10y + x

Simplify:

10x + y + 18 = 10y + x

⇒ 9x – 9y = –18 

⇒ x – y = –2   ...(2)

3. From equations (1) and (2): 

x + y = 8

x – y = –2

Add the two:

2x = 6

⇒ x = 3

Substitute (x = 3) in (1):

3 + y = 8

⇒ y = 5

4. The number is:

10x + y = 10 × 3 + 5

10x + y = 35

The required two-digit number is 35.