Question

sum of digits of two digit number is 12 if the number obtained by reversing is 18 more than the original number , and the find the original number ¿?​

Answer 1

Answer :

$\sf{ \star \: \: The \: original \: number \: is \: 57. \: \: \star }$

Explanation :

✦ Given :–

• Sum of a two digit number is 12.
• Number obtained by reversing the digits will be 18 more than the Original Number.

✦ To Find :–

• The Original Number.

✦ Solution :–

Let the First digit of the Original Number be x and the Second digit be y .

→ According to the First Condition :-

  x + y = 12  ------------(1)

→ According to the Second Condition :-  

=> 10y + x = 18 + ( 10x + y )

=> 10y + x = 10x + y + 18

=> 10y - y + x - 10x = 18

=> 9y - 9x = 18

=> 9 ( y - x ) = 18

=> y - x = ( 18 ÷ 9 )

=> - ( x - y ) = 2

=> x - y = ( -2 )

=> x = y - 2 -------------(2)

Putting the Value of 'x' from Equation(2)  in Equation(1) :

=> ( y - 2 ) + y = 12

=> y + y - 2 = 12

=> 2y = 12 + 2

=> 2y = 14

=> y = 14 ÷ 2

=> y = 7

Now , we have to find the both digits of the number.

➨ First Digit ( x ) = y - 2 = 7 - 2 = 5

➨ Second Digit ( y ) = 7

We have First Digit as 5 and the Second as 7.

∴ The number is 10x + y = 10(5) + 7 = 50 + 7 = 57

______________

☆ Additional Information :-

We write a two-digit number in the form of 10x + y where x is first digit and y is the second digit.

Let's take an example :

Let say we take a number 42

We will write it in the form of 10x + y.

10(4) + 2 where first digit is 4 and the second digit is 2.

Answer 2

step by step explained :

ORIGINAL ANSWER IS 57

Let unit place is x and tenth place is y so

Condition 1

x +y = 12

Condition 2 if digit Reversed

y +10x = x + 10y -18

y + 10x -x - 10y= -18

9x -9y = -18

9y -9x =18

9y- 9(12–y)= 18

9y-108+9y=18

18y= 18+108

y = 126/18

y= 7

So x = 12–7 =5

Original number = 10x +y = 10x5+7= 57

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