Common Registration Assessment, Part 1
Finding the volume of diluent to add
Practise reverse dilutions, starting from a stock and a target strength to find how much diluent to add, with three original worked questions.
Published 10 October 2026. Independent revision material, not GPhC questions, not for patient care.
A forward dilution asks for the final strength. A reverse dilution asks the opposite: you know the stock and the target strength, and you must find the final volume, then the amount of diluent to add.
The amount of active substance does not change during dilution, so stock volume x stock strength = final volume x final strength. The diluent is the final volume minus the stock volume, not the final volume itself.
The examples are fictional and practise the arithmetic only.
The method
- Write stock volume x stock strength = final volume x final strength.
- Solve for the final volume.
- Subtract the stock volume to get the diluent to add.
- Convert strengths to the same form before dividing, for example both as percentages.
- Check the answer is larger than zero and smaller than the final volume.
Three practice questions
Work each one on paper first, then open the answer. All drugs and patients are fictional.
Question 1
You have 50 mL of a fictional 10% w/v solution. How much diluent must be added to make a 2% w/v solution?
Show the answer
Answer: 200 mL
Working: Final volume = 50 x 10 / 2 = 250 mL. Diluent to add = 250 - 50 = 200 mL.
Question 2
You have 100 mL of a fictional 1 in 50 solution. How much diluent makes a 1 in 200 solution?
Show the answer
Answer: 300 mL
Working: 1 in 50 = 2% and 1 in 200 = 0.5%. Final volume = 100 x 2 / 0.5 = 400 mL. Diluent to add = 400 - 100 = 300 mL.
Question 3
You have 25 mL of a fictional 40% w/v glucose solution. How much water gives a 5% w/v solution?
Show the answer
Answer: 175 mL
Working: Final volume = 25 x 40 / 5 = 200 mL. Water to add = 200 - 25 = 175 mL.
Two subtractions save marks
Write final volume on one line and diluent to add on the next. The answer the question wants is almost always the second line.
Where marks are lost
- Answering with the final volume instead of the volume to add.
- Comparing a ratio strength with a percentage without converting one of them.
- Dividing the strengths the wrong way round so the final volume comes out smaller than the stock.
Frequently asked questions
How do I check a reverse dilution quickly?
The product of volume and strength must be the same before and after. If 50 mL x 10% does not equal 250 mL x 2%, something has gone wrong.
Does it matter what the diluent is?
Not for the arithmetic. The question will name the diluent, and the volume to add is the same whatever it is.
Sources
- The Pharmaceutical Journal, medication maths: dilutions
- The Pharmaceutical Journal, preparing for the GPhC pharmaceutical calculations assessment
- GPhC, 2026 assessment specification and permitted items
The questions above are original and use fictional drugs. PreRegExamPrep is not affiliated with or endorsed by the General Pharmaceutical Council.
Practise until the method is automatic
Try 15 free questions with worked answers. No sign-up required.
More calculation topics
- Dose by weight calculations for the GPhC assessment
- Volume to give: liquid medicine calculations
- Percentage strength calculations: w/v, w/w and ratios
- Dilution calculations with C1V1 = C2V2
- Infusion rate calculations in mL per hour
- Drip rate calculations: drops per minute
- Body surface area calculations
- Creatinine clearance (Cockcroft-Gault) calculations
- Moles and millimoles calculations
- Displacement volume calculations for reconstitution
- Quantity to supply calculations
- Using a provided formula in calculations
- Dose information from packaging and labels
- Diluting a stock to a lower strength
- Medicine cost and switch calculations
- Rounding rules in calculations
- Enteral feed rate calculations
- Electrolyte content over time
- Infusion dose per kg per hour
- Rounding doses to measurable volumes
- Relative risk and relative risk reduction
- Absolute risk reduction and number needed to treat
- Odds ratio and confidence intervals
- Relative versus absolute risk reduction
- Loading dose and volume of distribution
- Top-up doses from measured drug levels
- Salt correction factors
- Mass and molar drug concentrations
- Half-life and falling drug levels
- Steady-state concentration and infusion rate
- Bioavailability and equivalent oral doses
- Oral maintenance dose and dosing interval
- Elimination rate constant and half-life
- Accumulation towards steady state
- Ratio strengths and one in X
- Serial dilution factors
- Mixing solutions of different strengths
- Tablet quantities for reducing regimens
- Equivalent doses from provided conversion tables
- Thresholds and dose-banding algorithms
- Unit conversions for mass and volume
- Units and units per mL
- Reconstituting powders and final concentration
- Millimoles and milliequivalents
- Infusion time and volume remaining
- Days supply from pack sizes
- Percentage w/v and w/w conversions
- Ideal and adjusted body weight from formulae
- Diluting creams and ointments by weight
- Scaling a formula to a batch size
- Age-band doses from a provided table
- Tablet fractions and split doses
- Stones, pounds, inches and metric conversions
- Micrograms per minute from mg per hour
- Percentage change and mark-up
- Molar solutions and mass per volume
- Osmolarity from component concentrations
- Direct proportion and cross-multiplication
- Scientific notation and very small quantities
- Stock use and reorder quantities
- Parts per million and very dilute solutions
- Sodium chloride equivalents and isotonic solutions
- Density and specific gravity conversions
- Doses per day and hours between doses
- Capping a dose at a stated maximum
- Whole vials and ampoules to draw up
- Reading values from a provided graph
- Micrograms per kg per minute infusions
- Percentage composition of a compound preparation
See also the formula sheet, the eight sample questions and the approved calculator page.