Three quantities blended — Aptitude Question
Three quantities blended: 10 kg at ₹20, 20 kg at ₹30 and 20 kg at ₹40 are mixed. What is the average price per kg? Answer and worked solution on CodeKairo.
- Topic: Mixtures & Alligation
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
10 kg at ₹20, 20 kg at ₹30 and 20 kg at ₹40 are mixed. What is the average price per kg?
Options
- ₹30
- ₹32
- ₹34
- ₹36
Show the answer and the worked solution
Correct answer: B. ₹32
Worked solution
- Cost = 10 × 20 + 20 × 30 + 20 × 40 = 200 + 600 + 800 = ₹1,600.
- Weight = 50 kg.
- Average = 1,600 ÷ 50 = ₹32.
Answer: ₹32.
The idea
Weighted average across any number of components: total cost divided by total quantity. The plain mean of 20, 30 and 40 is 30 and is wrong.
Shortcut. Take ₹30 as the base: 10 kg at −10 and 20 kg at +10 net +₹100 over 50 kg, which is +₹2 — so ₹32.
Common trap. "₹30" — averaging 20, 30 and 40 plainly, ignoring that the dearest grade comes in twice the quantity of the cheapest.