The correct option is (B) 27.
Explanation:
Let the tens and the units digits of the required number be x and y, respectively.
Let the number be 10x + y.
Now,
10x + y = 3(x +y)
10x + y = 3x + 3y
10x - 3x = 3y - y
7x = 2y
7x - 2y = 0 .........(i)
Given that if 45 is added to it, the digits are reversed.
(10x + y)+ 45 = (10y + x)
10x + y + 45 = 10y + x
10x - x + y - 10y = -45
9x - 9y = -45
9(x - y) = -45
x - y = -45/9
x - y = -5 .........(ii)
Multiplying (i) by 1 and (ii) by 2, we gets
7x - 2y = 0 ………(iii)
2x - 2y = -10 ……..(iv)
Subtracting (iv) from (iii), we get
7x – 2x = 10
5x = 10
x = 10/5 = 2
Putting x = 2 in (i), we get
7x - 2y = 0
7 x 2 - 2y = 0
14 - 2y = 0
-2y = -14
y = -14/-2 = 7
Number = (10x + y)
= 10 x 2 + 7
= 20 + 7
= 27