Question

A two digit number is such that the product of its digit is 8. When 18 is subtracted from the number, the digits interchange its place. Find the numbers.

Answer 1

Let this two digit number be xy. Which means x=10x (as it comes in tens digit). 

Then as per the question, 

xy = 8, ....... (i) 

l0x + y - 18 = 10y + x 

⇒ 9x-9y-18=0 

⇒  x - y - 2 = 0 ....... (ii) 

Putting x = `8/"y"` from (i) in (ii) , we get ,

`8/"y" - "y" - 2 = 0`

⇒ y² + 2y - 8 = 0 

⇒ (y-2)(y+4 ) =O 

⇒ y = 2, hence from (i), x=4. 

Hence the number is 42