Question

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. 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

Answer 2

Answer:

x=1,y=2

Step-by-step explanation:

X + Y is = 9 ................(1)

9 (10 X + Y) = 2 ( 10 Y + x ) .......(2)

from (2):

90x+9y=20y+2x

88x=11y

x=y/8

by substituting x in (1)

(y/8)+y=9

y+8y=72

9y=72

y=8

substituting y:

x+y=9

x+8=9

x=1