Question

The sum of the digits of a two- digit number is 6. When we interchange the digits, the new number is 18 less than the original number. Find the original number.
( I want step by step explanation )​

Answer 1

Answer:

Answer is 5 + 1 that is 6

when we interchange we get 15 which is less than 18

Answer 2

Answer:

The original number is 42.

Step-by-step-explanation:

Let tens digit of the number be x.

And the unit digit of the number be y.

∴ The original number = xy

⇒ The original number = 10x + y

Also,

Number obtained by interchanging the digits = yx

∴ New number = 10y + x

From the first condition,

x + y = 6

⇒ x = 6 - y

⇒ x = - y + 6 - - - ( 1 )

From the second condition,

Original number = New number + 18

⇒ 10x + y = 10y + x + 18

⇒ 10x + y - 10y - x = 18

⇒ 10x - x + y - 10y = 18

⇒ 9x - 9y = 18

⇒ x - y = 2 - - - [ Dividing by 9 ]

⇒ ( - y + 6 ) - y = 2 - - - [ From ( 1 ) ]

⇒ - y + 6 - y = 2

⇒ - 2y = 2 - 6

⇒ - 2y = - 4

⇒ 2y = 4

⇒ y = 4 ÷ 2

⇒ y = 2

By substituting y = 2 in equation ( 1 ), we get,

x = - y + 6 - - - ( 1 )

⇒ x = - 2 + 6

⇒ x = 4

Now,

The original number = 10x + y

⇒ The original number = 10 * 4 + 2

⇒ The original number = 40 + 2

⇒ The original number = 42

∴ The original number is 42.