Question

A two-digit number is such that the product of the digits is 12. When 36 is added to the number the digits interchange their places. Determine the number.

Answer 1

Number is 26.

Step-by-step explanation:

Let x be the first digit and y be the second digit of a two-digit number. The number will be 10x +y.

Given:

xy = 12  

y = 12/x -------------(1)

10x + y +36 = 10y + x

9x - 9y = -36

Dividing by 9, we get x - y = -4 -------------(2)

Substituting y = 12/x in (2), we get: x -12/x = -4

x² -12 = -4x

x² +4x -12 = 0

x² +6x -2x - 12 = 0

x (x - 6) -2 (x - 6) = 0

(x - 2) (x -6) = 0

X can be +2 or +6

Y can be +6 or +2

So the number is 26.