the sum of digit of a two digit number is 8 if their digit are interchange the new number is increase by 18 than the original number find the original number
Answers
Answer:
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Step-by-step explanation:
ANSWER:-
Given:
The sum of digit of a two digit number is 8, If their digit are interchange the new number is increase by 18 than the original number.
To find:
The original number.
Solution:
Let the digit at units place be x &
Let the digit at tens place be y.
So,
Original number =10x + y.
The sum of the digits of a two-digit number is 8.
=) x + y = 8............(1)
If the digits are reversed, the new number is 18 increase than the original number.
=) 10y + x = 18 + 10x +y
=) 10y -y + x -10x = 18
=) 9y - 9x = 18
=) y - x = 2..............(2)
Substitution Method:
From equation (1), we get;
=) x + y = 8
=) y= 8-x...........(3)
Eliminate the value of y in equation (2), we get;
=) 8 - x -x = 2
=) 8 - 2x = 2
=) -2x = 2 -8
=) -2x= -6
=) x = -6/-2
=) x= 3
Putting the value of x in equation (3), we get;
=) y = 8 - 3
=) y = 5
Therefore,
Original number= 10x + y
=) 10(3) + 5
=) 30 +5
=) 35
Thus,
The original number is 35.