the sum of digit of a two digit number is 8. The number obtained by interchanging it's digit is 18 more than the original number. Find the original number.
Answers
Answer:
35
Step-by-step explanation:
x + y =8 -------(1)
10y +x = 18 + 10x + y
y-x = 2 ------(2)
solve equations (1) and (2)
x = 3 and y =5
The original number is 35
EXPLANATION.
Sum of digit of a two digit number is 8.
The number obtained by interchanging it's digit is 18 more than the original number.
As we know that,
Let the one number be = x.
Let other number be = y.
Sum of digit of a two digit number is 8.
⇒ x + y = 8. - - - - - (1).
Let, the original number be = 10x + y.
Let, interchanging number be = 10y + x.
The number obtained by interchanging it's digit is 18 more than the original number.
⇒ 10x + y = 10y + x + 18.
⇒ 10x + y - 10y - x = 18.
⇒ 9x - 9y = 18.
⇒ x - y = 2. - - - - - (2).
From equation (1) & (2), we get.
Adding both the equation, we get.
⇒ x + y = 8. - - - - - (1).
⇒ x - y = 2. - - - - - (2).
We get,
⇒ 2x = 10.
⇒ x = 5.
Put the value of x = 5 in the equation (1), we get.
⇒ x + y = 8.
⇒ 5 + y = 8.
⇒ y = 8 - 5.
⇒ y = 3.
Values of x = 5 and y = 3.
Original number be = 10x + y.
⇒ 10x + y = 10(5) + 3 = 50 + 3 = 53.
Interchanging number be = 10y + x.
⇒ 10y + x = 10(3) + 5 = 30 + 5 = 35.