A two-digit number is such that the product of its digits is 12. If 36 is added to the given number, then digits of given number interchange their places. The given number is equal to -

Correct option is D

Given:
· A two-digit number where the product of its digits is 12.
· When 36 is added to the number, the digits of the number interchange their places.
Formula Used:
· Let the two-digit number be 10x+y, where xis the tens digit and y is the units digit.
· Given that xy=12
· After adding 36, the number becomes 10y+x
Solution:
1. Given: 10x + y + 36 = 10y + x
9x − 9y = −36 or x – y = −4 (Equation 1)
The product of the digits is given by:
xy = 12 (Equation 2)
From Equation 1:
x = y − 4
Substitute x = y − 4 in Equation 2:
(y − 4) y = 12
y2−4y−12=0
Solving this quadratic equation:

Y = 6 or y = −2 (Negative digit not possible)
So, y=6 and from x = y−4, we get x=2
Therefore, the original number is:
10x + y = 10(2) + 6 = 26
· 26+36=62, which is indeed the number with the digits interchanged.