Question

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

Also, 

10y + x = 2xy 

⇒ 10y + 2y = 2.2y.y   ...[From (i)]

⇒ 12y = 4y² 

⇒ y = 3  

From (i), we get : 

x = 2 × 3

= 6 

∴ Original number = 10 × 3 + 6

= 36