How to Solve Three-Liquid Mixture Ratio Problems
Solve three-liquid mixture ratio problems using the share-sum and unit-share methods, with a worked example and practice questions with answers.
Expected Interview Answer
A three-liquid mixture in ratio a:b:c splits a total volume into three shares — a/(a+b+c), b/(a+b+c), and c/(a+b+c) — and every three-liquid problem reduces to finding this common sum and applying it consistently.
The method extends the two-liquid case: sum all three ratio parts to get the total number of shares, then each liquid’s quantity is its part times total volume divided by the shares sum. When a fourth condition is given, such as one liquid’s absolute quantity, use it to solve for the unit-share value first, then derive the other two liquids from that unit. When two three-liquid mixtures are merged, add each of the three components separately across both mixtures before forming the new combined ratio — this generalizes directly from the two-liquid combining rule. Always double-check that the three parts you compute sum back to the original total volume.
- The share-sum method scales cleanly from two to three (or more) components
- Solving for the unit-share value handles problems with a known absolute quantity
- Combining multiple three-part mixtures is just component-wise addition
AI Mentor Explanation
A 30-player academy splits into batters, bowlers, and all-rounders in ratio 3:2:1, giving 6 shares total, so batters get 3/6 of 30 = 15, bowlers 2/6 of 30 = 10, and all-rounders 1/6 of 30 = 5. If instead only the all-rounder count of 5 were given, dividing 5 by its 1-share value fixes the unit share at 5, letting you derive batters as 3×5=15 and bowlers as 2×5=10 without knowing the total upfront. This unit-share-first method is exactly how three-liquid ratio problems are solved when one absolute quantity is known.
Worked example
Total shares
- 5+3+1 = 9
Liquid A & B
- A = 50L
- B = 30L
Liquid C
- C = 10L
Step-by-Step Explanation
Step 1
Sum the ratio parts
For ratio a:b:c, total shares = a+b+c.
Step 2
Compute each fraction
Each liquid’s share is its part divided by the total shares.
Step 3
Handle a known absolute quantity
If one liquid’s quantity is given, divide it by its part number to find the unit-share value.
Step 4
Combine multiple mixtures
Add each of the three components separately across mixtures before forming the new ratio.
What Interviewer Expects
- Correct summation of three ratio parts into total shares
- Applying the unit-share method when one quantity is known
- Component-wise addition when combining multiple three-part mixtures
- Verifying computed quantities sum back to the stated total
Common Mistakes
- Forgetting to sum all three parts before computing fractions
- Applying the two-liquid method without adjusting for the third component
- Averaging ratios across mixtures instead of adding actual quantities
- Misassigning which part corresponds to which liquid
Best Answer (HR Friendly)
“For a three-liquid ratio, I add all three parts to get the total number of shares, then each liquid is its part divided by that total, multiplied by the total volume. If I am given one liquid’s actual quantity instead of the total volume, I divide that quantity by its part number to find what one share is worth, then scale the other two liquids from that unit. When combining multiple three-part mixtures, I add each of the three components separately across every mixture before forming the final ratio.”
Follow-up Questions
- How would you extend this method to four or more liquids?
- What changes if the problem gives a percentage instead of a ratio?
- How do you solve when the total volume is unknown but one ratio and one quantity are given?
- How would you verify a computed three-part answer is correct?
MCQ Practice
1. A 72-litre mixture has three liquids in ratio 3:2:1. How much of the second liquid is present?
Total shares = 6; second liquid = 2/6 × 72 = 24 litres.
2. Three liquids are in ratio 4:3:2. If the third liquid measures 12 litres, what is the total mixture volume?
Third part = 2 shares = 12L, so 1 share = 6L. Total shares = 9, so total volume = 9×6 = 54 litres.
3. A mixture of 100L has liquids in ratio 5:4:1. The combined quantity of the first two liquids is?
First two parts = 5+4 = 9 of 10 shares, so 9/10 × 100 = 90 litres.
Flash Cards
How to find total shares for ratio a:b:c? — Sum the parts: total shares = a+b+c.
How to use a known absolute quantity? — Divide it by its own part number to find the unit-share value.
How to combine two three-part mixtures? — Add each of the three components separately, then form the new ratio.
How to check your answer? — Confirm the three computed quantities sum to the stated total volume.