Question

The sum of the digits of a two digits' number is 12. If the new number formed by

number.

reversing the digit is greater than the original number by 18. Find the original number.​

Answer 1

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..

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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..

Step-by-step explanation:

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