How to Solve Two-Liquid Mixture Ratio Problems
Solve two-liquid mixture ratio problems by converting ratios to fractions and combining quantities, with a worked example and practice questions.
Expected Interview Answer
Mixing two liquids in a given ratio means splitting a total volume proportionally, so if liquid A and liquid B are combined in ratio a:b, liquid A occupies a/(a+b) of the total volume and liquid B occupies b/(a+b).
The core move is converting a ratio into fractions of the whole: for ratio a:b, the parts sum to a+b, and each liquid’s share is its part divided by that sum. When a mixture problem gives a total volume and a ratio, multiply the total by each fraction to get individual quantities. When two different mixtures are combined, treat each mixture’s liquid-A content as a separate quantity, add the liquid-A amounts across both, and add the totals, then re-express as a ratio or percentage. Always keep units consistent (litres, kilograms) before combining.
- One ratio-to-fraction conversion solves every split-volume question
- Combining two mixtures reduces to adding component quantities directly
- Prevents errors from treating ratios as raw quantities
AI Mentor Explanation
A team’s squad is split into batters and bowlers in a 3:2 ratio across 25 players, so batters get 3/5 of 25 = 15 and bowlers get 2/5 of 25 = 10, exactly how a two-liquid mixture splits a total volume by its ratio parts. If a second squad of 20 players has a 1:3 batter-to-bowler ratio, combining both squads means adding batters together and bowlers together separately before forming a new combined ratio. Never average the two ratios directly; always add the actual counts first.
Worked example
Total volume
- 20 litres
- Ratio A:B = 3:2
Liquid A
- 3/5 × 20 = 12 litres
Liquid B
- 2/5 × 20 = 8 litres
Step-by-Step Explanation
Step 1
Convert ratio to fractions
For ratio a:b, liquid A is a/(a+b) of the total, liquid B is b/(a+b).
Step 2
Apply to total volume
Multiply the total volume by each fraction to get individual quantities.
Step 3
Combining two mixtures
Add each liquid’s actual quantity across both mixtures separately, never average the ratios.
Step 4
Re-express as a ratio
Divide the combined quantities by their highest common factor to state the final ratio.
What Interviewer Expects
- Correct ratio-to-fraction conversion
- Applying fractions to a stated total volume
- Adding component quantities, not averaging ratios, when merging mixtures
- Simplifying the final combined ratio correctly
Common Mistakes
- Averaging two ratios directly instead of adding actual quantities
- Mixing units (litres with millilitres) before combining
- Applying the wrong fraction to the wrong liquid
- Forgetting to simplify the final ratio to lowest terms
Best Answer (HR Friendly)
“I convert the given ratio into fractions of the total — for a ratio of a to b, one liquid is a over a-plus-b of the total, and the other is b over a-plus-b. I multiply the total volume by each fraction to get exact quantities. If two mixtures are being combined, I always add the actual quantities of each liquid separately across both mixtures, then form the new ratio from those summed totals — I never average the two original ratios directly.”
Follow-up Questions
- How do you find the ratio after removing some mixture and replacing it with water?
- How would you solve for an unknown ratio given the final combined volume?
- What changes when the two mixtures have different total volumes?
- How do you verify a combined ratio is fully simplified?
MCQ Practice
1. A 30-litre mixture has milk and water in ratio 2:1. How much milk does it contain?
Milk fraction = 2/3, so milk = 2/3 × 30 = 20 litres.
2. Mixture X (10L, ratio 1:1) is combined with Mixture Y (20L, ratio 3:1) of the same two liquids. What is the combined ratio of liquid A to liquid B?
X gives 5:5, Y gives 15:5. Combined A = 20, B = 10, ratio 20:10 = 2:1.
3. A mixture of 40 litres has two liquids in ratio 3:5. The quantity of the second liquid is?
Second liquid fraction = 5/8, so 5/8 × 40 = 25 litres.
Flash Cards
How to convert a ratio a:b into fractions? — Liquid A = a/(a+b), Liquid B = b/(a+b) of the total.
How to combine two ratio mixtures? — Add each liquid’s actual quantity separately, then form the new ratio — never average the ratios.
What must match before combining volumes? — Units (litres, kilograms) must be consistent across both mixtures.
Final step after combining quantities? — Simplify the combined ratio by dividing out the highest common factor.