Question

the sum of the digits of a two-digit number is 6 on reversing its digit the number is 18 less than the original number find the number​

Answer 1

Answer:

• The original number is 42.

Given:

• The sum of the digits of a two digit number is 6.

• On reversing its digit the number is 18 less than the original number.

To find:

• The original number.

Solution:

Let the unit's place of the two digit number be y and the ten's place be x.

According to the first condition.

⠀⠀>> x+y = 6...(1)

Original number = 10x + y

Number with reversed digits = 10y + x

According to the second condition.

⠀⠀=> 10x + y = 10y + x + 18

⠀⠀=> 9x - 9y = 18

⠀⠀>> x - y = 2...(2)

Add equations (1) and (2), we get

⠀⠀ x + y = 6

+

⠀⠀ x - y = 2

⠀⠀_______

⠀⠀=> 2x = 8

⠀⠀=> x = 4

Substitute x = 4 in equation (1), we get

⠀⠀4 + y = 6

⠀⠀=> y = 2

Original number = 10(4) + 2 = 42

Therefore, the original number is 42.