The sum of the digits of a two-digit number is 4. Nine times of this number is equal the number obtained by reversing the order of the digits. Find the number.
Answers
Step-by-step explanation:
Given :-
The sum of digits f a two digit number is 9.
Also nine times this number is twice the number obtained by reversing the order of digit.
To Find :-
The Number
Solution :-
Let the unit digit and tens digits of the number be x and y
Number = 10y + x
Number after reversing the digits = 10x + y
According to the question,
⇒ x + y = 9 ... (i)
⇒ 9(10y + x) = 2(10x + y)
⇒ 88y - 11x = 0
⇒ -x + 8y =0 ... (ii)
Adding equation (i) and (ii), we get
⇒ 9y = 9
⇒ y = 1 ... (iii)
Putting the value in equation (i), we get
⇒ x = 8
Hence, the number is 10y + x = 10 × 1 + 8 = 18.