# What will be the unit digit?

A two digit number is such that the product of the digits is 12. When 36 is added to this number, the digits interchange their place. The unit digit would be:

- 2
- 4
- 6
- None of these

**Answer: (c) 6
Explanation:-
**Let the two digit number be = XY

this means, the real number is = 10X + Y

Product of the digits XY = 12 …….(1)

According to question, 10X + Y + 36 = 10Y + X

9X – 9Y = – 36

X – Y = – 4

From equation (1), 12/Y – Y = – 4

12 – Y^{2} = – 4Y

Y^{2} – 4Y – 12 = 0

Y^{2} – 6Y + 2Y – 12 = 0

Y(Y – 6) + 2(Y – 6) = 0

(Y +2)(Y – 6) = 0

Y + 2 = 0 and Y – 6 = 0

Y = – 2 and Y = 6

Hence, the number is 26 and the unit digit is 6.