Common Registration Assessment, Part 1
Mixing solutions of different strengths
Calculate the final strength when two solutions are combined, using conserved drug mass and stated final volumes.
Published 7 October 2026. Independent revision material, not GPhC questions, not for patient care.
Two solutions of the same drug can both contribute to the final amount. Unlike dilution with water, the second solution is not necessarily drug-free. Calculate the amount in each portion, add those amounts, then divide by the final volume.
These questions assume additive volumes and no loss or reaction. Under those conditions, final concentration = (C1 × V1 + C2 × V2) ÷ (V1 + V2). In a real preparation, compatibility and the final measured volume need checking. Arithmetic alone is not a compounding instruction.
The method
- Convert both strengths to the same unit.
- Multiply each concentration by its own volume.
- Add the amounts, not just the concentrations.
- Divide total amount by final volume.
- Check that final strength lies between the starting strengths.
Three practice questions
Work each one on paper first, then open the answer. All drugs and patients are fictional.
Question 1
Mix 100 mL of a 2 mg/mL solution with 300 mL of a 6 mg/mL solution of the same drug. Volumes are additive. Find final concentration.
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Answer: 5 mg/mL
Working: Amounts are 200 mg and 1,800 mg. Total = 2,000 mg in 400 mL. Strength = 5 mg/mL.
Question 2
Mix 50 mL of 4% w/v solution with 150 mL of 1% w/v solution of the same substance. Volumes are additive. Find final percentage w/v.
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Answer: 1.75% w/v
Working: Amounts are 4 × 50 ÷ 100 = 2 g and 1 × 150 ÷ 100 = 1.5 g. Total = 3.5 g in 200 mL, or 1.75 g in 100 mL.
Question 3
To make 200 mL at 5 mg/mL, mix 10 mg/mL and 2 mg/mL solutions of the same drug. Volumes are additive. How much stronger solution is needed?
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Answer: 75 mL
Working: Let x mL be the stronger solution. 10x + 2(200 − x) = 1,000. Thus 8x = 600, so x = 75 mL. Check: 750 + 250 = 1,000 mg in 200 mL.
The mass-balance idea
The Pharmaceutical Journal dilution method tracks concentration and volume through containers. The same conserved-amount approach extends to these original mixing exercises, where both starting containers contain drug.
Where marks are lost
- Averaging strengths without accounting for unequal volumes.
- Treating the weaker solution as water.
- Adding strengths instead of amounts.
Frequently asked questions
When is the simple average correct?
When equal volumes are mixed under the stated additive-volume assumptions. Otherwise use the volume-weighted calculation.
Can final strength exceed both starting strengths?
Not under these assumptions. That result suggests a mass, volume or unit error.
Sources
- The Pharmaceutical Journal, medication maths: dilutions
- 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
- Tablet quantities for reducing regimens
- Equivalent doses from provided conversion tables
- Thresholds and dose-banding algorithms
See also the formula sheet, the eight sample questions and the approved calculator page.