The sum of the digits of a two digits’ number is 12. If the new numb

1.	The sum of the digits of a two digits’ number is 12. If the new number formed by reversing the digit is greater than the original number by 18. Find the original number.
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..

The sum of the digits of a two digits’ number is 12. If the new number formed by reversing the digit is greater than the original number by 18. Find the original number.

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..