RUŌOD Lab

Level 5 · Perfume Mathematics and Formula Design

Perfume Dilution Practice Problems

A harder drill set on dilutions: mixing two strengths, stepping down in stages, recovering a batch and working backward from a finished perfume, with answers.

Intermediate 35 min study By the RUŌOD Lab team Updated

In short

Most dilution problems reduce to one idea: track the pure material, since it does not change when you add solvent. This drill set goes beyond a simple dilution to mixing strengths, recovering mistakes and working backward. The dilution equation gives the general form, C1 × W1 = C2 × W2.

What you will learn

  • Solve mixed-strength dilution problems
  • Work backward from a finished strength
  • Recover a dilution that came out wrong

Before this lesson: Normalize a Formula to 1,000 Parts

The problems

1. You want 40 g at 2.5% from a 10% stock. 10 g stock + 30 g solvent.

2. You weighed 3.00 g of stock at 5% into a 30.00 g total. What strength is it? 0.15 ÷ 30 = 0.5%.

3. You mix 5 g at 20% with 15 g at 2%. What strength is it? Pure 1.0 + 0.3 = 1.3 g in 20 g: 6.5%.

4. You want 10 g at 8%, using 20% and 1% stocks only. How much of each? Let x be grams of 20%: 0.2x + 0.01(10 − x) = 0.8. So 0.19x = 0.7, x = 3.68 g of the 20%, and 6.32 g of the 1%. No extra solvent.

5. You made 15 g that you thought was 10%, but the weighing log shows 1.80 g of material. What is its strength, and how much solvent brings it to 10%? 12%. 1.80 ÷ 0.10 = 18 g total, so add 3 g.

6. The same batch, but it reads 1.20 g of material. Can you reach 10% by adding solvent? What can you add? It is 8%, weaker than you want, so solvent cannot help. To 15 g at 8%, add x g of neat material: (1.2 + x) ÷ (15 + x) = 0.10, x = 0.33 g.

7. A stock bottle labeled 10% weighed 20.00 g when made, and now weighs 17.50 g. Alcohol has evaporated, and no material has been taken out. What is the true strength? 2 g of pure material in 17.50 g: 11.4%.

8. You need 0.003 g of pure material on a 0.01 g scale with a 0.2 g practical minimum. Choose a stock. 0.003 ÷ 0.2 = 1.5% maximum. Use 1%, weighing 0.30 g.

9. A 100 g perfume is to hold 12 g of concentrate that is 75% active. What is its active strength? 9 g of active in 100 g: 9%.

10. You must make that perfume at 12% active instead. How much concentrate? 12 ÷ 0.75 = 16 g, and 84 g of alcohol.

How to attack any of these

  1. Write down what you know as pure material.
  2. Write what the target is as pure material and total.
  3. Check whether you can get there by adding solvent. You cannot dilute upward.
  4. Check the answer: do pure and total give the wanted strength?

Problem 7 is the one people forget in practice. A stock can become stronger simply by losing solvent, and the stock solutions lesson explains how a gross weight on the label catches it. Problem 6 shows why adding too much of a material is usually easier to fix than adding too little, and the guide on adding too much of an ingredient extends the idea to whole formulas.

Practical exercise: Solve the drill set

About 45 minutes · You will have: ten worked problems, and a note on which type you find hardest

  1. Work all ten without looking, then check. Show your method.
  2. For each miss, name the step where you went wrong.
  3. Choose problem 4 or 6, change the numbers and solve it again.
  4. Use the calculators in the dilution basics lesson to check two simple answers. They do not solve the mixed-strength ones, so those must come from you.

You have done this well if you get at least eight right, and the checks in step 4 of the method pass for each.

Common mistakes

  • Trying to dilute upward. Solvent cannot raise a strength.
  • Averaging percentages without weights. 20% and 2% only average to 11% at equal weights.
  • Ignoring evaporation in old stocks. The label records a past state.

Key terms

Blending strengths
Mixing two dilutions of one material to reach a strength between them.

Knowledge check

1. You mix 10 g at 10% with 10 g at 1%. What strength results?
Show the answer

5.5%. Pure: 1 g + 0.1 g = 1.1 g in 20 g, or 5.5%.

2. You made 10 g at 12%, but wanted 10%. How much solvent do you add?
Show the answer

2 g. You have 1.2 g of pure material. For 10%, the total must be 12 g, so add 2 g.

3. How many steps down from neat to 0.01%, by factors of 10?
Show the answer

4. 10%, 1%, 0.1% and 0.01%.

Further reading and materials

Written and reviewed by the RUŌOD Lab team. This is general education, not legal, regulatory, medical or safety advice. Example dilutions and exercises are for learning, are not validated products, and have not been safety-assessed. Completing a lesson confers no qualification. How we check these lessons.