Question

the sum of the digits of the two digit number is 12.the number obtained by interchanging the digits exceeds the given number by 18.find the number. ​

Answer 1

Given :-

• Sum of the digits of the required number = 12
• The number obtained by interchanging the digits exceeds the original number by 18

To Find :-

• The original number.

Solution :-

Let x and y be the two digits of the original number. If we consider x as the ten's digit and y as the unit's digit, the original number would be: 10x + y and the reversed number would be 10y + x.

A.T.Q,

⇒ x + y = 12......( 1 )

Also,

⇒ 10x + y + 18 = 10y + x

⇒ 10y + x - 10x -y = 18

⇒ 9y - 9x = 18

⇒ y - x = 2.......( 2 )

Adding ( 1 ) & ( 2 ),

⇒ 2y = 14

⇒ y = 7

Putting the value of y in ( 1 ),

⇒ x + 7 = 12

⇒ x = 12 - 7 = 5

Therefore,

• Value of x (ten's digit) = 5
• Value of y (unit's digit) = 7

Then,

The required two-digit number would be:

⇒ 10 × 5 + 7

⇒ 50 + 7 = 57.

Answer 2

Let the ten's digit and the one's digit be x and y respectively.

Given

The sum of the digits of the two digit number is 12.

$\implies x+y=12--(1)$

The number obtained by interchanging the digits exceeds the given number by 18.

$\implies 10y+x=10x+y+18\\\implies 10y+x-10x-y=18\\\implies-9x+9y=18\\\implies x-y=-18--(2)$

Solving (1) and (2), we get,

$x+y=12\\\underline{x-y=-2}\\\underline{\underline{2x=10}}\\\implies x = 5$

$\implies y = 7$

$\boxed{\boxed{\bold{Therefore, \ the \ required \ number \ is \ 57}}}}}}}}$