Question

the sum of digits of a two digit number is 12.if 18 is added to the number the digits are reserved. find the original number​

Answer 1

Answer:

let the number be x

$x + x = 12 \\ 2x = 12 \\ x = \frac{12}{2} \\ x = 6 \\ x + 18 \\ = 6 + 18 \\ 24$

Answer 2

Answer:

The original number is 57.

Step-by-step-explanation:

Let the digit at the tens place be x.

And the digit at the units place be y.

∴ The original number = 10x + y

The number obtained by interchanging the digits = 10y + x

From the first condition,

x + y = 12

⇒ x = 12 - y

⇒ x = - y + 12 - - ( 1 )

From the second condition,

The original number + 18 = The number obtained by interchanging the digits

10x + y + 18 = 10y + x

⇒ 10x + y - 10y - x = - 18

⇒ 9x - 9y = - 18

⇒ x - y = - 2 - - [ Dividing by 9 ]

⇒ ( - y + 12 ) - y = - 2 - - [ From ( 1 ) ]

⇒ - y + 12 - y = - 2

⇒ - 2y = - 2 - 12

⇒ - 2y = - 14

⇒ 2y = 14

⇒ y = 14 ÷ 2

⇒ y = 7

By substituting y = 7 in equation ( 1 ), we get,

x = - y + 12 - - ( 1 )

⇒ x = - 7 + 12

⇒ x = 5

Now,

The original number = 10x + y

⇒ The original number = 10 ( 5 ) + 7

⇒ The original number = 50 + 7

∴ The original number is 57.