Question

A two-digit number is such that the product of its digits is 14. If 45 is added to the number, the digit interchange their places. Find the number. 

 

Answer 1

Let the digits at units and tens places be x and y, respectively. 

∴` xy=14` 

⇒`y=14/x`                      ...............(1) 

According to the question: 

`(10y+x)+45=10x+y` 

⇒`9y-9x=-45` 

⇒`y-x=5`                 ...................(2) 

From (1) and (2), we get 

`14/x-x=-5` 

⇒`(14-x^2)/x=-5` 

⇒`14-x^2=-5` 

⇒`x^2-5x-14=0` 

⇒`x^2-(7-2)x-14=0` 

⇒`x^2-7x+2x-14=0` 

⇒`x(x-7)+2(x-7)=0` 

⇒`(x-7)(x+2)=0` 

⇒`x-7=0  or  x+2=0` 

⇒`x=7  or  x=-2` 

⇒`x=7`              (∵the digit cannot be negative) 

Putting x =7 in equation (1), we get 

`y=2` 

∴ Required number=`10xx2+7=27`