The sum of the digits of a two-digit number is 11. When the digits are reversed, the number increases by 27. Find the original number.
the original number is?
Answers
Given :
• The sum of the digits of a two digit number = 11
• When the digits are reversed, the number increases by 27
To find :
• The original number
Solution :
Let the two digit number be 10x + y
where,
- x and y are the digits
According to the first condition given in the question :-
→ x + y = 11 -------(1)
According to the second condition given in the question :-
→ 10y + x = 27 + 10x + y
→ 10y - y = 10x - x + 27
→ 9y = 9x + 27
→ Taking 9 common from both the sides :-
→ 9(y) = 9(x + 3)
→ Cancelling 9 from both the sides :-
→ y = x + 3
→ x - y + 3 = 0
→ x - y = - 3 -------(2)
Solving 1 and 2 :-
→ x + y = 11
→ x - y = - 3
__________
→ 2x = 8
__________
→ 2x = 8
→ x = 8 ÷ 2
→ x = 4
Substitute the value of x in equation (1) :-
→ x + y = 11
→ 4 + y = 11
→ y = 11 - 4
→ y = 7
Therefore, the value of x = 4 and y = 7
The original number is :-
→ 10x + y
→ 10(4) + 7
→ 40 + 7
→ 47
Therefore, the original number is 47