The sum of the digits of two digit number is 12.If the new number formed by reversing the digits is greater than the original by 18, find the original number.
Answers
Step-by-step explanation:
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..
Answer:
The original number is 57.
Step-by-step explanation:
Solution :
[tex][/tex]
In Original number -
- Units digit as y
- Tens digit as 10(12 - y)
Original Number = 10(12 - y) + y
Number with reversed digits -
- Units digit = (12 - y)
- Tens digit = 10(y)
According to the Question,
The new number formed by reversing the digits is greater than the original by 18
⇒ 10(12 - y) + y + 18 = 10y + 12 - y
⇒ 120 - 10y + y + 18 = 9y + 12
⇒ 138 - 9y = 9y + 12
⇒ 138 - 12 = 9y + 9y
⇒ 126 = 18y
⇒ y = 126/18
⇒ y = 7
Original number =
⇒ 10(12 - 7) + 7
⇒ 50 + 7
⇒ 57
Therefore, the original number is 57.