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:

  1. 2
  2. 4
  3. 6
  4. None of these
Monis Rasool Professor Asked on 27th May 2015 in Maths.
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1 Answer(s)

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 – Y2 = – 4Y
Y2 – 4Y – 12 = 0
Y2 – 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.

Anurag Mishra Professor Answered on 28th May 2015.
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