Pharmaceutical Calculations Demystified: Exam-Ready Solutions for Pharmacists
pharmaceutical calculations questions and answers


Note:: First try your best to solve these pharmaceutical calculations. If you find them difficult you can consult the step-by-step solutions at the end of the MCQ questions.





26) What is the micrograms/mL concentration of a solution of Dopamine (Inotropin) containing 200mg in 500ml of Normal Saline and ordered to be administered to a 155-pound patient at a rate of 5 micrograms/kg/min?
a- 0.4 micrograms/mL
b- 40 micrograms/mL
c- 200 micrograms/mL
d- 400 micrograms/mL
e- 1200 micrograms/mL

Solution:

To calculate the concentration of the Dopamine solution in micrograms/ml, we need to convert the weight of the patient from pounds to kilograms and use the prescribed dosage of 5 micrograms/kg/min.

Convert the weight of the patient from pounds to kilograms:
155 lbs ÷ 2.2046 lbs/kg = 70.31 kg

Calculate the total dosage of Dopamine per minute:
5 micrograms/kg/min x 70.31 kg = 351.55 micrograms/min

Calculate the total dosage of Dopamine per ml:
200 mg = 200,000 micrograms (since 1 mg = 1000 micrograms)
200,000 micrograms ÷ 500 ml = 400 micrograms/ml

Therefore, the concentration of the Dopamine solution in micrograms/ml is 400 micrograms/ml.

Thus the correct answer is d.






27) If the IV solution contains 15,000 units of Heparin per 250ml of Normal Saline and an administration set has a drop factor of 60 drops per ml, what is the number of drops per minute required to achieve an infusion rate of 20 units of Heparin per minute?
a- 20
b- 40
c- 60
d- 80
e- 120

Solution:

To determine the number of drops per minute needed to administer 20 units of Heparin per minute, we need to first calculate the rate of infusion in ml per minute and then convert it to drops per minute.

Calculate the rate of infusion in ml per minute:
15,000 units/250 ml = 60 units/ml

1ml / 60 units x 20 units = 0.333 ml per minute

With an infusion rate of 0.333 ml per minute, the patient will be receiving 20 units of heparin.

Convert ml per minute to drops per minute using the administration set's drop factor:
0.333 ml per minute x 60 drops per ml = 20 drops per minute

Therefore, approximately 20 drops per minute are needed to administer 20 units of Heparin per minute with an administration set delivering 60 drops per ml.

Thus the correct answer is a.







28) The following is the hospital formula for a T-A-C solution:
Cocaine HCL 4%
Tetracaine HCL 2%
Epinephrine HCL solution 1/2000
Sodium Chloride injection q.s 4ml

Calculate the number of milligrams of Cocaine HCL present in the final solution?
a- 40 mg
b- 400 mg
c- 200 mg
d- 80 mg
e- 160 mg

Solution:

To find out how many mg of Cocaine HCL are in the final solution, you can follow these steps:

Convert the percentage concentration to a decimal: 4% = 0.04

Multiply the decimal by the total volume of the solution (4 mL) to find the amount of Cocaine HCL in the solution:
0.04 * 4 mL = 0.16 mL

Since 1 mL of a substance contains 1000 mg, multiply the volume by 1000 to get the amount in mg:

0.16 mL * 1000 mg/mL = 160 mg

So, there are 160 mg of Cocaine HCL in the final solution.

Thus the correct answer is e.








29) The following is the hospital formula for a T-A-C solution:
Cocaine HCL 4%
Tetracaine HCL 2%
Epinephrine HCL solution 1/2000
Sodium Chloride injection q.s 4ml

How many ml of Adrenaline Chloride solution (0.1%) may be used to prepare the solution?
a- 2 ml
b- 0.04 ml
c- 1 ml
d- 0.002 ml
e- 5 ml

Solution:

To determine how many mL of Adrenaline Chloride solution (0.1%) may be used to prepare the T-A-C solution, you first need to find out the amount of Epinephrine HCL that is required.

Convert the percentage concentration of Epinephrine HCL to a decimal: 

1/2000 = 0.0005

Multiply the decimal by the total volume of the solution (4 mL) to find the amount of Epinephrine HCL in the solution:

0.0005 * 4 mL = 0.002 mL

Since 1 mL of a substance contains 1000 mg, multiply the volume by 1000 to get the amount in mg:

0.002 mL * 1000 mg/mL = 2 mg

Now, you need to find out how many mL of Adrenaline Chloride solution (0.1%) are required to provide 2 mg of Epinephrine HCL.

Convert the percentage concentration of Adrenaline Chloride solution (0.1%) to a decimal: 

0.1% = 0.001

Divide the required amount of Epinephrine HCL (2 mg) by the concentration of Adrenaline Chloride solution (0.001) to find the volume in mL:

2 mg / 0.001 = 2,000 µL (microLiters)

Convert µL to mL: 2,000 µL = 2 mL

So, you may use 2 mL of Adrenaline Chloride solution (0.1%) to prepare the T-A-C solution.

Thus the correct answer is a.










30) Using one quart of water, a pharmacist dilutes 100ml of Clorox. Determine the W/V ratio of Sodium Hypochlorite in the resulting dilution, given that commercial Clorox has a Sodium Hypochlorite concentration of 5.25% W/V.
a- 1/6
b- 1/16
c- 1/120
d- 1/160
e- 1/200

Solution:

First, we need to convert the volume of water from quarts to milliliters since the initial volume of Clorox is given in milliliters.

1 quart = 946.35 ml (approximately)

Therefore, the total volume of the final dilution is:

100 ml + 946.35 ml = 1046.35 ml

Next, we can calculate the amount of Sodium Hypochlorite (NaClO) in the initial 100 ml of Clorox:

Since commercial Clorox has a Sodium Hypochlorite concentration of 5.25% W/V;

5.25 / 100 = 0.0525

Amount of NaClO = 100 ml x 0.0525 = 5.25 g

Since we added 946.35 ml of water, the concentration of NaClO in the final solution can be calculated as:

Concentration of NaClO = 5.25 g / 1046.35 ml = 0.005 (or 0.5% or 1/200 W/V)

Therefore, the W/V ratio of Sodium Hypochlorite in the final dilution is 0.5% or 1/200 W/V.

Thus the correct answer is e.





31) What is the total daily dose of Zidovudine, in milligrams, for a 180-pound patient when the prescribed adult intravenous (IV) dose is 2mg per kg of body weight, administered every 4 hours, six times a day?
a- 10 mg
b- 175 mg
c- 500 mg
d- 750 mg
e- 980 mg

Solution:

First, we need to convert the weight of the patient from pounds to kilograms:

180 lb / 2.205 = 81.63 kg

The patient's weight is 81.63 kg.

Next, we can calculate the total daily dose of Zidovudine using the formula:

Total daily dose = Dose per kg x Body weight x doses per day

The dose per kg is 2 mg/kg
The patient's weight is 81.63 kg
The doses per day are 6

Total daily dose = 2 mg/kg x 81.63 kg x 6 = 979.59 mg

Therefore, the patient will receive a total of 979.59 mg of Zidovudine daily.

Thus the correct answer is e.








32) If a prescription for 4% Pilocar solution instructs the patient to use "Gtt I OU TID" (one drop in each eye three times daily), how much Pilocarpine HCL is being consumed per day? It can be assumed that the dropper dispenses 20 drops per ml.
a- 4 mg
b- 8 mg
c- 12 mg
d- 24 mg
e- 48 mg

Solution:

To calculate the amount of Pilocarpine HCL used per day, we need to know the concentration of Pilocarpine HCL in the 4% Pilocar solution.

A 4% solution means that there are 4 grams of Pilocarpine HCL in 100 ml of solution. Therefore, the concentration of Pilocarpine HCL in the 4% Pilocar solution is:

4 grams / 100 ml = 0.04 grams/ml = 40 mg/ml

The prescription calls for one drop in each eye, three times a day. So the total number of drops per day is:

2 eyes x 1 drop x 3 times = 6 drops per day

If the dropper is calibrated to deliver 20 drops per milliliter, then the volume of solution delivered by one drop is:

1 ml / 20 drops = 0.05 ml per drop

Therefore, the amount of Pilocarpine HCL in one drop of the 4% Pilocar solution is:

40 mg/ml x 0.05 ml per drop = 2 mg per drop

The total amount of Pilocarpine HCL used per day is the amount in one drop multiplied by the total number of drops per day:

2 mg per drop x 6 drops per day = 12 mg per day

Therefore, the patient is using approximately 12 mg of Pilocarpine HCL per day.

Thus the correct answer is c.








33) How many micrograms of Digoxin are in 3 ml of Lanoxin pediatric elixir, which has a concentration of 0.05 mg/ml?
a-  0.15 micrograms
b- 1.5 micrograms
c- 15 micrograms
d- 150 micrograms
e- 300 micrograms

Solution:

Each milliliter (ml) of Lanoxin pediatric elixir contains 0.05mg of Digoxin.

To convert mg to micrograms (mcg), we need to multiply by 1000 since 1 mg is equal to 1000 mcg.

So, 0.05 mg = 0.05 x 1000 mcg = 50 mcg

Therefore, 3 ml of Lanoxin pediatric elixir contains:

3 ml x 50 mcg/ml = 150 mcg

Thus the correct answer is d.








34) What is the percentage concentration of Sodium Fluoride in a community's drinking water if the concentration is 0.6 ppm?
a- 0.00006%
b- 0.0006%
c- 0.006%
d- 0.06%
e- 0.6%

Solution:

To express the concentration of Sodium Fluoride in a community's drinking water as a percentage, we need to convert parts per million (ppm) to percentage (%).

One ppm is equivalent to one part per million parts or 1/1,000,000, which can also be expressed as 0.0001%.

1/1,000,000 x 100 = 0.0001%

To convert ppm to percentage, we can use the following formula:

Concentration (ppm) x 0.0001 = Concentration (%)

So for a concentration of 0.6 ppm of Sodium Fluoride, we can calculate the percentage as follows:

0.6 ppm x 0.0001 = 0.00006%

Therefore, the concentration of Sodium Fluoride in the community's drinking water is 0.00006%.

Thus the correct answer is a.










35) During a week, blood pressure measurements were taken for five patients, and their average readings were as follows:

Patient 1: 140/70 mmHg
Patient 2: 160/84 mmHg
Patient 3: 180/88 mmHg
Patient 4: 190/90 mmHg
Patient 5: 150/70 mmHg

What is the median systolic pressure?
a- 88
b- 86
c- 160
d- 180
e- 164

Solution:

To find the median systolic pressure, we need to first arrange the systolic pressure values in ascending or descending order.

In this case, the systolic pressure values are:

140, 160, 180, 190, 150

Arranging them in ascending order, we get:

140, 150, 160, 180, 190

The median is the middle value when the values are arranged in order. In this case, we have an odd number of values, so the median is the middle value, which is:

160

Therefore, the median systolic pressure is 160 mmHg.

Thus the correct answer is c.











36) A package insert lists a drug dose for a neonate as being 10 micrograms/kg/day. The age range for a 'neonate' is generally considered to be?
a- The first 28 days of life
b- 1 month to 6 months
c- The first 1 week of life
d- 1 year through 5 years
e- the first year of life

Solution:

The age range for a neonate varies depending on the source, but it is generally considered to be the first 28 days of life. After that, the infant is considered an infant until the age of 12 months.

In this case, the drug dose listed for a neonate is 10 micrograms per kilogram per day, which means that it is the appropriate dose for a newborn who weighs a certain amount. The dose may need to be adjusted as the infant grows and gains weight.

Thus the correct answer is a.








37) If the drug dose is 5 mg per kilogram of body weight, what would be the appropriate dose for a female patient weighing 110 pounds?
a- 125 mg
b- 250 mg
c- 500 mg
d- 750 mg
e- 75 mg

Solution:

To calculate the dose for a 110-lb female patient, we first need to convert the weight from pounds to kilograms:

110 lbs ÷ 2.205 = 49.9 kg

Now that we have the weight in kilograms, we can calculate the dose:

Dose = 5 mg/kg x 49.9 kg = 249.5 mg

Therefore, the dose for a 110-lb female patient should be 249.5 mg.

Thus the correct answer is b.








38) If Drug X has a dosage of 65 mg per kilogram of body weight, what would be the appropriate dose for a child weighing 35.2 pounds?
a- 12.5 mg
b- 186.5 mg
c- 250 mg
d- 300 mg
e- 1037.4 mg

Solution:

To calculate the dose for a child who weighs 35.2 pounds, we need to first convert the weight to kilograms:

35.2 pounds ÷ 2.205 = 15.96 kg

Now we can calculate the dose:

Dose = 65 mg/kg x 15.96 kg = 1037.4 mg

Therefore, the appropriate dose of Drug X for a child who weighs 35.2 pounds would be 1037.4 mg.

Thus the correct answer is e.









39) What is the amount of drug present in a 5 mL solution ampule with a concentration of 0.2%?
a- 0.1 mg 
b- 1 mg 
c- 10 mg 
d- 100 mg 
e- 1000 mg  

Solution:

To calculate the amount of drug in a 5 mL solution ampule with a concentration of 0.2%, we need to know the strength or quantity of the drug in the solution.

If we assume that the concentration of 0.2% refers to the weight/volume percentage (w/v), meaning that there is 0.2 grams of the drug in 100 mL of solution, we can calculate the amount of drug in the 5 mL solution ampule as follows:

Amount of drug per ml = 0.2 g / 100 mL = 0.002 g/mL

Amount of drug per 5 ml = 0.002 g/mL x 5 mL = 0.01 g

0.01 g = 10 mg

Therefore, the amount of drug in a 5 mL solution ampule with a concentration of 0.2% is 0.01 grams (or 10 milligrams).

Thus the correct answer is c.










40) What is the total amount of the drug in five teaspoons of an elixir, if the concentration of the drug is 0.2%?
a- 5 mg
b- 10 mg
c- 15 mg
d- 30 mg
e- 50 mg

Solution:

If the concentration of a drug is 0.2%, it means that there are 0.2 grams of the drug in 100 ml of the solution. 

To calculate the amount of drug in 5 teaspoons of the solution, we need to know the volume of each teaspoon.

Assuming that each teaspoon is 5 mL, the total volume of 5 teaspoons would be:

5 teaspoons x 5 mL/teaspoon = 25 mL

To calculate the amount of drug in 25 mL of the solution with a concentration of 0.2%, we can use the following formula:

Amount of drug = concentration x volume

In this case, the concentration is 0.2% or 0.002 (in decimal form), and the volume is 25 mL:

Amount of drug = 0.002 x 25 mL = 0.05 grams

0.05 grams = 50 milligrams

Therefore, the total amount of the drug in 25 mL of the solution is 50 milligrams.

Thus the correct answer is e.








41) What will be the weight of one gallon of a substance if its specific gravity is 1.25?
a- 125 grams
b- 590 grams
c- 1042 grams
d- 2.8 kilograms
e- 4731 grams

Solution:

The weight of one gallon depends on the substance being measured. However, if we assume that the substance has a specific gravity of 1.25, then we can calculate the weight of one gallon using the following formula:

Weight of one gallon = Volume of one gallon x Specific gravity

The volume of one gallon is equal to 128 fluid ounces or approximately 3.785 liters. Therefore, the weight of one gallon of a substance with a specific gravity of 1.25 would be:

Weight of one gallon = 3.785 liters x 1.25
Weight of one gallon = 4.73125 kilograms approximately.

4.73125 kilograms = 4731 grams

Thus the correct answer is e.









42) What is the correct method for preparing an 18% NaCl solution?
a) Dissolve 18 mg of NaCl in 100 ml of water
b) Dissolve 18 mg of NaCl in 100 ml of solvent
c) Dissolve 18 g of NaCl in 1000 ml of water
d) Dissolve 18 g of NaCl in 100 ml of water
e) Dissolve 18 g of NaCl in 1000 ml of solvent

Solution:

The correct method for preparing an 18% NaCl solution is to dissolve 18 grams of NaCl in 100 milliliters of water. 

To prepare the solution, weigh out 18 grams of NaCl using a digital scale and add it to a clean and dry container. 

Then, add about 80 ml of water to the container and stir well to dissolve the NaCl completely. 

Finally, add more water up to a final volume of 100 ml, and stir again to ensure that the solution is well-mixed. 

Thus the correct answer is d.




43) Fifty micrograms are equal to?
a- 50,000 nanograms
b- 0.005 milligrams
c- 0.00005 g
d- a and b 
e- a and c 

Solution:

Generally, we know that;

1 kg = 1000 g = 1000,000 mg = 1000,000,000 µg = 1000,000,000,000 ng

50,000 ng = 50 µg = 0.050 mg = 0.00005 g

Fifty micrograms (50 µg) is equal to 0.05 milligrams (0.05 mg) and 0.00005 grams (0.00005 g), which is equivalent to 50,000 nanograms (50,000 ng).

Thus the correct answer is e.





44) What is the weight/volume percentage (W/V) of a solution if it contains 3 grams of a drug per fluid ounce?
a- 1.0 %
b- 6.5 %
c- 10.1 %
d- 15.2 %
e- 25.3 %

Solution:

To determine the percentage w/v (weight/volume) of a solution, we need to know the weight of the solute (in grams) and the volume of the solution (in milliliters).

In this case, we are given that the solution contains 3 grams of a drug per fluid ounce. However, we need to convert fluid ounces to milliliters in order to calculate the percentage w/v.

One fluid ounce is equivalent to approximately 29.57 milliliters. 

Therefore, the weight/volume of the solution can be calculated as follows:

Weight of solute = 3 g
Volume of solution = 29.57 mL

Percentage w/v = (weight of solute ÷ volume of solution) x 100%
Percentage w/v = (3 g ÷ 29.57 mL) x 100%
Percentage w/v = 10.14%

Therefore, the percentage w/v of the solution is 10.14%.

Thus the correct answer is c.








45) What is the Fahrenheit (°F) equivalent of -10 degrees Celsius (°C)?
a- 10.4 °F
b- 12 °F
c- 14 °F
d- 5 °F
e- (-2)°F

Solution:

The formula to convert Celsius to Fahrenheit is:

°F = (°C x 1.8) + 32

Substituting -10 for °C, we get:

°F = (-10 x 1.8) + 32
°F = -18 + 32
°F = 14

Therefore, the correct answer is c.






46) What will be the concentration of the ointment if 15 grams of a drug are added to prepare an ointment with a total weight of 150 grams?
A) 10 %
B) 15 %
C) 18 %
D) 30 %
E) 150 % 

Solution:

let's think through this step-by-step:

You have an ointment with a total weight of 150gm

You have added 15gm of a drug to this ointment.

To calculate the concentration of the drug in the final ointment, we use the formula:

Concentration = (Weight of drug) / (Total weight of ointment)

So in this case:

Weight of drug = 15gm

Total weight of ointment = 150gm

Concentration = (15gm) / (150gm) = 0.1 = 10%

Therefore, the concentration of drug in the final ointment is 10%.

Therefore, the correct answer is a.









47) What is the procedure to prepare 100 ml of a 12% MgCl solution?
a- dissolve 12 ml of MgCl in 100 ml water
b- dissolve 12 mg of MgCl in 100 ml water
c- dissolve 12 g of MgCl in 100 ml water
d- dissolve 88 ml of MgCl  in 100 ml water
e- dissolve 88 mg of MgCl  in 100 ml water

Solution:

To prepare 100 ml of 12% MgCl solution, we need to know the amount of MgCl and the volume of water required to dissolve it. 

We can use the formula for calculating the concentration of a solution, which is:

Concentration = (Amount of solute / Volume of solution) x 100

We can rearrange this formula to find the amount of solute or the volume of solution needed, depending on what is given.

In this case, we know the final volume of the solution we want to prepare (100 ml) and the desired concentration (12%). We can use the formula to find the amount of MgCl needed:

Amount of MgCl = Concentration x Volume of solution / 100

Amount of MgCl = 12 x 100 / 100 = 12 g

Therefore, to prepare 100 ml of 12% MgCl solution, we need 12 grams of MgCl. 

Here are the steps to prepare 100 ml of 12% MgCl solution:

Weigh 12 grams of MgCl using a balance and add it to a suitable container.

Add about 80 ml of distilled or deionized water to the container and stir the mixture until the MgCl is completely dissolved.

Add more water (up to 100 ml) to the container to make up the final volume and stir the mixture again.

Transfer the solution to a storage container (such as a glass bottle) and label it with the concentration and the date of preparation.
 
Therefore, the correct answer is c.







48) What would be the total amount of drug administered to a 70kg patient over a period of 12 hours, if the infusion rate is 2mg/kg/hr?
a- 660 mg
b- 880 mg
c- 1150 mg
d- 1440 mg
e- 1680 mg

Solution:

The total dose of the drug infused for 12 hours at a rate of 2mg/kg/hr in a 70kg patient can be calculated as follows:

Calculate the total dose per hour:
2mg/kg/hr x 70kg = 140mg/hr

Calculate the total dose infused over 12 hours:

Total dose = dose per hour x infusion time

Total dose = 140mg/hr x 12 hr = 1680mg

Therefore, the total dose of the drug infused for 12 hours in a 70kg patient at a rate of 2mg/kg/hr is 1680mg.

Therefore, the correct answer is e.






49) What is the quantity of drugs in grains required to prepare a 5% (w/v) solution having a volume of 4 fluid ounces?
a- 9.25 grains
b- 92.5 grains
c- 192.5 grains
d- 255.6 grains
e- 925 grains

Solution:

You want to make 4 fluid ounces of a 5% (W/V) drug solution

5% (W/V) means 5 grams of drug per 100 mL of solution

1 fluid ounce = 29.5735 mL

So 4 fluid ounces = 4 * 29.5735 mL = 118.294 mL

Since the concentration is 5% (W/V), for every 100 mL of solution you need 5g of drug

For 118.294 mL of solution, you will need 

(5g / 100 mL) x 118.294 mL = 5.9147 g = ~6g of drug

Converting grams into grains;

To convert 6 grams of the drug into grains, we can use the conversion factor 

1 gram = 15.432 grains.

Therefore,

6 grams = 6 x 15.432 grains = 92.592 grains

Thus, 6 grams of drug is equal to approximately 92.592 grains.

Therefore, the correct answer is b.







50) What is the percent W/W of the active ingredient in an ointment weighing 110g, which is prepared by adding 10g of white petroleum?
a- 10 %.
b- 9.09 %.
c- 0.71 %.
d- 0.95 %.
e- 100 %

Solution:

The percent W/W of the active ingredient in an ointment weighing 110g and containing 10g of white petroleum is calculated as follows:

Percentage of active ingredient = (Weight of active ingredient / Total weight of ointment) x 100

= (10g / 110g) x 100

= 9.09%

Therefore, the percent w/w of the active ingredient in the ointment is 9.09%.

Therefore, the correct answer is b.