Site icon Noon Academy

A two digit positive number is such that the product of its digits is

   

. If

   

is added to the number, the digits interchange their places. Find the number. (2014)

Let us consider

   

-digit number be ‘xy’ =

   

Reversed digits = yx =

   

So according to the question,

   

It is given that,

   

so, by substituting the value in above equation, we get

   

By taking LCM,

   

Divide by

   

, we get

   

let us factorize,

   

So,

   

Value of x =

   

[since,

   

is a negative value]

Now, substitute the value of x in y =

   

, we get

   

   

-digit number =