First, work out how much you actually need to give the patient
5mg per Kg.
If the patient is 80 Kg, they need 80 times the amount needed for 1Kg (i.e. 80 x 5mg).
Be careful though, as that is the amount over 120 mins, whereas your options for answers are all flow rate per hour. This will not matter, as we will see, but just bare that in mind that you need to amount over two hours, not one.
You now know how much is needed over a two hour period.
Then, work out how much of the concentration you need to give them.
There is 30mg per mL of sterile concentrate.
Say for example you got an answer of 150mg in the first part, that is the total amount required. If you divide this total amount by 30, it will tell you how many mL must be administered per hour. 150/30 = 5mL of aminodarone
You now know how much of the concentration you must give them over two hours.
Finally, work out which concentration will actually give them that amount. Fortunately, the answers have been very kind!
Using B as an example, if you add 6mL aminodarone to 500mL sodium chloride, you now have a 506 mL solution. If you administer 253 mL per hour and you have 506 mL solution, you give 253 in hour 1, have 253 left over that you will give in hour two, so it takes two hours to give the full 6mL aminodarone. In other words:
Amount of aminodarone + amount of solution = total amount of solution
Flow rate / total amount of solution = time to administer total amount of solution
Hint: You will find they all last the same amount of time apart from one. You will also find that they conveniently all fit into a round number of hours, no minutes left over anywhere!
A couple more things to notice to actually work out the answer then:
The ones that have 250mL solution are more concentrated. For example D and E both have 8 mL in glucose, however D is in 250 mL glucose, so 32 mL added to 1L, whereas E is in 500 m,L glucose, so 16 mL added to 1L.
The solutions that you are adding them to are different. Some are glucose, some are sodium chloride.
I am not a doctor/nurse in training so I don't know what impact those two things would have on a patient, so I will leave that to your capable medical hands to work out why one is more suitable than the other!