State true or false:
The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. The number is 18.
True
Let the unit digit and tens digits of the number be x and y respectively.
Then, the number will be 10y+x
Number after reversing the digits is 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