Question

A two-digit number is 4 times the sum of its digits and twice the product of digits. Find the number. 

Answer 1

Let the digits at units and tens places be x and y, respectively.
Original number =10y + x
According to the question 

`10y+x=4(x+y)` 

⇒`10y+x=4x+4y` 

⇒`3x-6y=0`  

⇒`3x=6y` 

⇒`x=2y`                ............(1) 

Also 

`10y+x=2xy` 

⇒`10y+2y=2.2yy`                               [from(1)]

⇒`12y=4y^2` 

⇒`y=3`  

From (1), We get : 

`x=2xx3=6` 

∴ Original number=`10xx3+6=36`