Question

A two digit number is such that the product of its digit is 2 if9 is added to the number, the digits interchange their places. find the number

Answer 1

Let the digits be x and y

Then the two-digit number is 10x + y

Given that xy = 2 ----------1

10x + y +9 = 10y + x    

9y - 9x = 9

y - x = 1

y = x + 1 ----------------2

Substitute the value of y in eqn 1

x (x+1) = 2

x2 + x – 2 = 0

x2 - x + 2x – 2 = 0

x (x-1) + 2 (x-1) = 0                                                                                                                                     

(x + 2) (x – 1) = 0

x = -2 or x = 1

Since the x cannot take negative value

x = 1

therefore, y = 2

The number is 10x + y = 10 * 1 + 2 = 12.

Answer: The two-digit number is 12.