The digit of a 2-digit number differ by 5. If the digits are interchanged and the resulting number is added to the original number, we get 99. Find the original number.
Answers
Answer:-
Let the number be (10x + y).
Given:
Difference of the digits = 5
→ x - y = 5 -- equation (1).
And,
The Sum of the number and number formed by interchanging the digits = 99
→ 10x + y + 10y + x = 99
→ 11x + 11y = 99
→ 11(x + y) = 99
→ x + y = 99/11
→ x + y = 9 -- equation (2).
Adding equations (1) & (2) we get,
→ 2x = 14
→ x = 14/2
→ x = 7
Substitute "x" value in equation (1).
→ x - y = 5
→ 7 - y = 5
→ y = 7 - 5
→ y = 2
The number = 10x + y = 10(7) + 2 = 72.
Hence, the Original number is 72.
QUESTION :
The digit of a 2-digit number differ by 5. If the digits are interchanged and the resulting number is added to the original number, we get 99. Find the original number.
ANSWER :
Let the digit in ten's.Place be x and the digit in the ones place be y.
∴x + y = 5 ⟶( i )
∴Two digit number = 10x + y
Two digit after reversing the digits = 10y + x
According to the question,
∴10x + y + 10y + x = 99
⇒11 x + 11y = 99
⇒x + y = 99 ⟶( ii )
On adding equation i) and ii)
2x = 14
x = 14÷2
x = 7
Putting the value of x in equation i)
x - y = 5
⇒y = 2
∴Number = 10 y + x
= 72