GPhC Pharmaceutical Calculations 2 — Questions and Answers
Question 1: A pharmacist needs to prepare 200mL of a 5% w/v solution from a 20% w/v stock solution and water. What volumes of stock solution and water are needed?
- 25mL stock + 175mL water
- 50mL stock + 150mL water (Correct answer)
- 100mL stock + 100mL water
- 40mL stock + 160mL water
Correct answer: 50mL stock + 150mL water
Using C₁V₁ = C₂V₂: 20% × V₁ = 5% × 200mL. V₁ = (5 × 200) ÷ 20 = 50mL of stock solution. Water needed = 200mL - 50mL = 150mL.
Question 2: An insulin pen delivers 100 units/mL. A patient is prescribed 36 units twice daily. How many days will a 3mL cartridge last?
- 2 days
- 4 days (Correct answer)
- 8 days
- 10 days
Correct answer: 4 days
Total units in cartridge = 100 units/mL × 3mL = 300 units. Daily dose = 36 units × 2 = 72 units/day. Days supply = 300 ÷ 72 = 4.17 days, so the cartridge will last 4 complete days.
Question 3: A prescription asks for coal tar solution 5% in aqueous cream to make 100g. The coal tar solution BP contains coal tar 20% w/w. How much coal tar solution BP is required?
- 5g
- 10g
- 20g
- 25g (Correct answer)
Correct answer: 25g
The final product needs 5% coal tar solution, i.e., 5g of coal tar solution in 100g. But the coal tar solution BP is 20% w/w coal tar. The prescription asks for 'coal tar solution 5%' — meaning 5g of coal tar solution BP per 100g total. Therefore 25g of coal tar solution BP is needed to provide 5g of actual coal tar (25g × 20% = 5g coal tar).
Question 4: A patient weighing 70kg requires gentamicin at 5mg/kg/day administered in two divided doses. Gentamicin injection is available as 80mg/2mL. What volume is needed per dose?
- 2.19mL
- 4.38mL (Correct answer)
- 8.75mL
- 3.5mL
Correct answer: 4.38mL
Daily dose = 5mg/kg × 70kg = 350mg. Per dose = 350 ÷ 2 = 175mg. Concentration = 80mg/2mL = 40mg/mL. Volume = 175mg ÷ 40mg/mL = 4.375mL, approximately 4.38mL.
Question 5: A pharmacist prepares 500mL of an oral solution. The displacement value of the suspended powder is 0.8mL/g, and 25g of powder is used. What volume of vehicle is needed?
- 475mL
- 480mL (Correct answer)
- 500mL
- 520mL
Correct answer: 480mL
Displacement volume of powder = 25g × 0.8mL/g = 20mL. The powder displaces 20mL when suspended. Therefore, vehicle needed = 500mL - 20mL = 480mL to give a final volume of 500mL.
Question 6: A prescription reads: 'Hydrocortisone cream 1% diluted 1 in 4 with aqueous cream. Supply 100g.' How much hydrocortisone 1% cream is needed?
- 4g
- 25g (Correct answer)
- 33g
- 75g
Correct answer: 25g
'Diluted 1 in 4' means 1 part hydrocortisone cream in 4 parts total (i.e., 1 part cream + 3 parts diluent). For 100g total: hydrocortisone cream = 100g ÷ 4 = 25g. Aqueous cream = 100g - 25g = 75g.
GPhC Pharmaceutical Calculations 2
A pharmacist needs to prepare 200mL of a 5% w/v solution from a 20% w/v stock solution and water.
What volumes of stock solution and water are needed?