Question

A two digit number is such that the product of the digit is 12. When 36 is added to the number

the digits interchange their places.​

Answer 1

is it number is equal to X

let the tens digit number is equal to y

product of the digit is 12

Answer 2

Let the ten's digit be x and unit's digit be y.
Number = 10x + y
xy=12 y = … (i)
Also, 10x+y+36 = 10y+x
9x-9y+36 = 0
x-y+4 = 0 … (ii)
From (i) and (ii),
x+4 =
x2+4x-12=0
(x+6)(x-2) =0
x=2 or x=-6
Rejecting x = -6, we have x = 2.
y= ==6
Thus, the required number is 2 x 10 + 6 = 26.