Alligation or Mixture — 18 Aptitude Questions and Answers with Explanations

Alligation or Mixture — Questions and Answers

Alligation is a visual shortcut for weighted averages: place the two ingredient values on the ends, the mean in the middle, and cross-subtract to get the mixing ratio. Its second use — the repeated replacement formula — appears in almost every bank exam: after n replacements of x litres from a vessel of V litres, the pure liquid left is V(1 − x/V)ⁿ.

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Alligation or Mixture— Concepts, Formulas & Shortcuts

Alligation rule: (cheaper qty)/(dearer qty) = (dearer price − mean)/(mean − cheaper price).
Replacement: after n operations of removing x from V and topping up, pure liquid left = V(1 − x/V)ⁿ.
Water is treated as a zero-cost ingredient when diluting to a target price.
Alligation works for any weighted average — price, percentage, speed, concentration.
Mixing equal quantities of two mixtures averages their fractions; mixing unequal quantities needs the weighted form.
Always confirm whether the ratio asked for is ingredient : ingredient or ingredient : total.

Alligation or Mixture Practice Questions with Answers

Attempt each question first, then open the explanation. All 18 questions below are free to read and require no signup.

Q1.In what ratio must rice at ₹15/kg be mixed with rice at ₹20/kg so that the mixture costs ₹18/kg?
Moderate
- A2 : 3
- B3 : 2
- C1 : 2
- D3 : 5
+Show Answer & Explanation
Answer: A. 2 : 3
Explanation: By alligation: (20 − 18) : (18 − 15) = 2 : 3.
Alligation or Mixture question 1 of 18
Q2.A vessel holds 40 litres of pure milk. 4 litres are removed and replaced with water, and the process is repeated once more. The milk left is:
Difficult
- A30.4 L
- B32 L
- C32.4 L
- D34 L
+Show Answer & Explanation
Answer: C. 32.4 L
Explanation: 40 × (1 − 4/40)² = 40 × 0.81 = 32.4 litres.
Alligation or Mixture question 2 of 18
Q3.60 litres of a mixture contain milk and water in the ratio 3 : 2. How much water must be added to make the ratio 1 : 1?
Moderate
- A10 L
- B12 L
- C15 L
- D18 L
+Show Answer & Explanation
Answer: B. 12 L
Explanation: Milk = 36 L, water = 24 L. For 1 : 1 water must be 36 L, so add 12 litres.
Alligation or Mixture question 3 of 18
Q4.A 40-litre mixture has milk and water in the ratio 3 : 1. The quantity of milk is:
Easy
- A24 L
- B28 L
- C30 L
- D32 L
+Show Answer & Explanation
Answer: C. 30 L
Explanation: Milk = 3/4 × 40 = 30 litres.
Alligation or Mixture question 4 of 18
Q5.In what ratio must water be mixed with milk costing ₹32 per litre to obtain a mixture worth ₹28 per litre?
Moderate
- A1 : 7
- B1 : 8
- C2 : 7
- D1 : 6
+Show Answer & Explanation
Answer: A. 1 : 7
Explanation: Water costs ₹0. By alligation: (32 − 28) : (28 − 0) = 4 : 28 = 1 : 7.
Alligation or Mixture question 5 of 18
Q6.Two alloys contain gold and copper in the ratios 5 : 3 and 5 : 11. Equal quantities are melted together. The ratio of gold to copper in the new alloy is:
Difficult
- A5 : 7
- B15 : 17
- C10 : 13
- D3 : 5
+Show Answer & Explanation
Answer: B. 15 : 17
Explanation: Gold fractions are 5/8 and 5/16; their mean is (10/16 + 5/16)/2 = 15/32. So gold : copper = 15 : 17.
Alligation or Mixture question 6 of 18
Q7.In what ratio must tea at ₹200/kg be mixed with tea at ₹300/kg to get a mixture worth ₹240/kg?
Moderate
- A2 : 3
- B3 : 2
- C4 : 5
- D5 : 4
+Show Answer & Explanation
Answer: B. 3 : 2
Explanation: By alligation: (300 − 240) : (240 − 200) = 60 : 40 = 3 : 2.
Alligation or Mixture question 7 of 18
Q8.A 50-litre mixture has milk and water in the ratio 4 : 1. The quantity of water is:
Easy
- A8 L
- B10 L
- C12 L
- D15 L
+Show Answer & Explanation
Answer: B. 10 L
Explanation: Water = 1/5 × 50 = 10 litres.
Alligation or Mixture question 8 of 18
Q9.How much water must be added to 60 litres of milk costing ₹20 per litre to reduce the cost to ₹15 per litre?
Difficult
- A15 L
- B20 L
- C25 L
- D30 L
+Show Answer & Explanation
Answer: B. 20 L
Explanation: By alligation, water : milk = (20 − 15) : (15 − 0) = 1 : 3. Milk is 60 L, so water = 20 litres.
Alligation or Mixture question 9 of 18
Q10.A vessel contains 60 litres of pure milk. 10 litres are removed and replaced with water. The milk remaining is:
Moderate
- A45 L
- B48 L
- C50 L
- D54 L
+Show Answer & Explanation
Answer: C. 50 L
Explanation: 60 × (1 − 10/60) = 60 × 5/6 = 50 litres.
Alligation or Mixture question 10 of 18
Q11.Two vessels contain milk and water in the ratios 2 : 1 and 3 : 2. Equal volumes are mixed. The ratio of milk to water in the mixture is:
Difficult
- A19 : 11
- B5 : 3
- C7 : 5
- D3 : 2
+Show Answer & Explanation
Answer: A. 19 : 11
Explanation: Milk fractions are 2/3 and 3/5; their mean is (10/15 + 9/15)/2 = 19/30, so milk : water = 19 : 11.
Alligation or Mixture question 11 of 18
Q12.In what ratio must a grocer mix rice at ₹30/kg and ₹45/kg so that the mixture is worth ₹36/kg?
Moderate
- A2 : 3
- B3 : 2
- C4 : 3
- D5 : 3
+Show Answer & Explanation
Answer: B. 3 : 2
Explanation: (45 − 36) : (36 − 30) = 9 : 6 = 3 : 2.
Alligation or Mixture question 12 of 18
Q13.In what ratio must sugar at ₹40/kg be mixed with sugar at ₹60/kg to get a mixture at ₹50/kg?
Easy
- A1 : 1
- B1 : 2
- C2 : 1
- D2 : 3
+Show Answer & Explanation
Answer: A. 1 : 1
Explanation: (60 − 50) : (50 − 40) = 10 : 10 = 1 : 1.
Alligation or Mixture question 13 of 18
Q14.A 20-litre mixture has milk and water in the ratio 3 : 2. The milk is:
Easy
- A8 L
- B10 L
- C12 L
- D15 L
+Show Answer & Explanation
Answer: C. 12 L
Explanation: Milk = 3/5 × 20 = 12 litres.
Alligation or Mixture question 14 of 18
Q15.How much water must be added to 30 litres of milk to make the milk-to-water ratio 3 : 1?
Moderate
- A8 L
- B10 L
- C12 L
- D15 L
+Show Answer & Explanation
Answer: B. 10 L
Explanation: For 3 : 1 with 30 L of milk, water must be 10 litres.
Alligation or Mixture question 15 of 18
Q16.A vessel holds 80 litres of pure milk. 20 litres are removed and replaced with water. The milk left is:
Moderate
- A50 L
- B55 L
- C60 L
- D65 L
+Show Answer & Explanation
Answer: C. 60 L
Explanation: 80 × (1 − 20/80) = 80 × 0.75 = 60 litres.
Alligation or Mixture question 16 of 18
Q17.In what ratio must water be mixed with milk costing ₹50 per litre to sell the mixture at ₹40 per litre (water is free)?
Moderate
- A1 : 4
- B1 : 5
- C2 : 5
- D1 : 3
+Show Answer & Explanation
Answer: A. 1 : 4
Explanation: (50 − 40) : (40 − 0) = 10 : 40 = 1 : 4.
Alligation or Mixture question 17 of 18
Q18.Two mixtures contain acid and water in the ratios 1 : 3 and 3 : 5. Equal volumes are mixed. The fraction of acid in the result is:
Difficult
- A5/16
- B1/2
- C3/8
- D7/16
+Show Answer & Explanation
Answer: A. 5/16
Explanation: Acid fractions are 1/4 and 3/8; their mean is (2/8 + 3/8)/2 = 5/16.
Alligation or Mixture question 18 of 18

Alligation or Mixture — Frequently Asked Questions

What is the repeated replacement formula?+

If x units are removed from V units of pure liquid and replaced with water, n times over, the pure liquid remaining is V(1 − x/V)ⁿ. Removing 4 L from 40 L twice leaves 40(0.9)² = 32.4 L of milk.

Can alligation be used for anything other than price?+

Yes — it is just the weighted-average rule. It works for concentrations, percentages, average speeds and average marks equally well.

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