Question

The sum of the digits of a 2 digit number is 12. If the new number formed by reversing the digits is greater than the original number by 18,find the original number .check the solution

Answer 1

let the 2 digit no. is 10x + y

x + y = 12 eq1

10y + x = 10x + y + 18

9y - 9x = 18

-x + y = 18 eq2

On adding eq 1 and eq2

2y = 30

x = 15

put y in eq1

x + 15 = 12

x = -3

No was 10x + y

= 10 × (-3) + 15 = -15

Hence the no. is -15



Thanks

Answer 2

Answer:

Let x be the unit digit and y be tens digit.

Then the original number be 10x+y.

Value of the number with reversed digits is 10y+x.

As per question, we have

x+y=12 ....(1)

If the digits are reversed, the digits is greater than the original number by 18.

Therefore, 10y+x=10x+y+18

⇒9x−9y=−18 ....(2)

Multiply equation (1) by 9, we get

9x+9y=108 ....(3)

Add equations (2)and (3),

18x=90

⇒x=5

Substitute this value in equation (1), we get

5+y=12⇒y=7

Therefore, the original number is 10x+y=10×5+7=57..