In the above question, a two digit number is supposed as 10y+x or 10x+y and solved as follows

And, y=x²

Let the two digit positive number be 10x+y

According to the question,  10x+y-(10y+x)=54

⇒ 9x-9y=54

⇒ x-y=6

As per the question y=x², So

⇒ x-x²=6

⇒ x-x²-6=0

⇒ x²-3x-2x-6=0

⇒ x(x-3)-2(x-3)=0

⇒ (x-2)(x-3)=0

⇒ x=2 or x=3

∴ y=x²  or y=4, 9

Number is either 24 or 39.

According to the question difference between the original number and the number obtained by interchanging the digits is 54

Here, 24 is not possible (42-24=18)

And 39 is the original number (93-39=54)

40% of the original number is

$39\times \frac{40}{100}=3.9\times 4=15.6$

Hence, Option A is correct.