CBSE Class 8 Answered

Let the 2 digits be x and y

Let the no. be 10x+y

Given,

       xy = 8  ( Product of 2 no.s)......(1)

    10x+y-18=10y+x  ..............................(2) (if 18 is subtracted from the original number then the new number will be in the opposite way)

x = 8/y.....(3).....from (1)

10x + y - 10y - x = 18

9x - 9y = 18

9(x - y) = 18

x - y = 2.........(4)... ....from  (2)

Substitute (3) in (4)

8/y-y=2

On taking LCM

8  -y²/y = 2

-y² - 2y + 8 = 0

y2+ 2y - 8 = 0

On splitting the middle term

y²+4y-2y-8

y(y + 4) - 2(y + 4)

y = -4 , 2

Since digit cannot be negative y = 2

So x= 8/y......   from (1)

x = 8/2 ........x = 4 

So the no.is 10x + y...

10×4 + 2 = 42

The no. is 42