A certain number of two digits is three times the sum of its digits and if 45 be added to it, the digits are reversed. The number is ?

A certain number of two digits is three times the sum of its digits and if 45 be added to it, the digits are reversed. The number is ? Correct Answer 27

Let the ten's digit be x and unit's digit be y
Then,
$$\eqalign{ & \Rightarrow 10x + y = 3\left( {x + y} \right) \cr & \Rightarrow 7x - 2y = 0.....(i) \cr & 10x + y + 45 = 10y + x \cr & \Rightarrow y - x = 5.....(ii) \cr} $$
Solving (i) and (ii), we get :
x = 2 and y = 7
∴ Required number = 27
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