Question

The sum of the digits of a 2digit number is 9. Also 9times the number is twice the number obtained by reversing the order of digits. Find the number.

Answer 1

Let unit digit = x
Tens digit = y
Number will 10 times the tens digit + unit times the unit digit
Hence number will 10 y + x

Sum of digits are 9
So that
X + y = 9 ………….(1)
nine times this number is twice the number obtained by reversing the order of the digits

9 (10 y + x ) = 2 (10 x + y )
90 y + 9 x = 20 x + 2y
88 y – 11 x = 0
Divide by 11 we get
8 y - x = 0 …………..(2)
X + y = 9 ………….(1)

Adding both equations we get
9 y = 9
Y = 9/9 = 1
Plug this value in equation first we get
X+ y = 9
X + 1 = 9
X = 8
So our original number is 10 y + x = 10*1 + 8 = 18


Hope you understand the solution 😀