Question

9 times a two-digit number is 2 times the number obtained by reversing its digits. the sum of digits is 9.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