Pariksha SaathiQuantitative Aptitude
Mixture and Alligation: Practice Questions with Answers
13 practice questions on Mixture and Alligation, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.
Read the lesson on this topic →
-
Q.1
Three varieties of rice costing ₹20/kg, ₹25/kg and ₹30/kg are mixed in quantities 10 kg, 20 kg and 30 kg respectively. Find the average price of the mixture.
Show answer
Answer: ₹26.67/kg (80/3)
Solution:
- With three components, use the weighted-average definition directly instead of the two-term alligation ratio.
- Total cost = (10 × 20) + (20 × 25) + (30 × 30) = 200 + 500 + 900 = ₹1,600
- Total quantity = 10 + 20 + 30 = 60 kg
- Average price = 1,600 / 60 = ₹26.67/kg (80/3)
-
Q.2
A mixture of 60 litres contains milk and water in the ratio 2 : 1. How much water must be added to make the ratio of milk to water 1 : 2?
Show answer
Answer: 60 litres
Solution:
- Milk = (2/3) × 60 = 40 L, Water = (1/3) × 60 = 20 L.
- Adding water doesn’t change the milk, so if x litres of water are added: 40 / (20 + x) = 1 / 2
- 80 = 20 + x → x = 60 litres. Check: 40 : (20 + 60) = 40 : 80 = 1 : 2.
-
Q.3
A container has 40 litres of pure milk. 8 litres are withdrawn and replaced with water, and this process is repeated once more. Find the quantity of pure milk left after the two operations.
Show answer
Answer: 25.6 litres
Solution:
- Each operation removes a fraction x/V = 8/40 = 1/5 of whatever is currently in the container.
- After n operations, pure liquid left = V × (1 − x/V)ⁿ = 40 × (1 − 1/5)² = 40 × (4/5)²
- = 40 × 16/25 = 25.6 litres
-
Q.4
A milkman mixes water (free) with milk and sells the mixture at the same price as pure milk, thereby gaining 20%. Find the ratio of water to milk in the mixture.
Show answer
Answer: 1 : 5 (water : milk)
Solution:
- Let the price of pure milk (and the selling price of the mixture) = ₹6/litre. A 20% gain means the mixture’s own cost price = SP ÷ 1.2 = 6 ÷ 1.2 = ₹5/litre.
- Apply alligation with water (₹0) as the "cheaper" item and milk (₹6) as the "dearer" item, mean = ₹5: water : milk = (6 − 5) : (5 − 0) = 1 : 5.
-
Q.5
In what ratio should tea worth ₹60/kg be mixed with tea worth ₹80/kg so that the mixture is worth ₹65/kg?
Show answer
Answer: 3 : 1 (₹60/kg tea : ₹80/kg tea)
Solution:
- Using the alligation rule: cheaper : dearer = (80 − 65) : (65 − 60) = 15 : 5 = 3 : 1.
- Check: weighted average = (3 × 60 + 1 × 80) / 4 = (180 + 80) / 4 = 260/4 = 65 — matches.
-
Q.6
A trader mixes 20 kg of rice costing ₹40/kg with 30 kg of rice costing ₹60/kg. Find the average price of the mixture.
Show answer
Answer: ₹52/kg
Solution:
- Total cost = (20 × 40) + (30 × 60) = 800 + 1,800 = ₹2,600
- Total quantity = 20 + 30 = 50 kg
- Average price = 2,600 / 50 = ₹52/kg
-
Q.7
Rice at ₹18/kg, ₹24/kg and ₹30/kg is mixed in quantities 5 kg, 10 kg and 15 kg. Find the average price of the mixture.
Show answer
Answer: ₹26/kg. Total cost = 90+240+450 = 780; total qty = 30; 780/30.
-
Q.8
In what ratio should rice worth ₹50/kg be mixed with rice worth ₹70/kg so that the mixture is worth ₹55/kg?
-
Q.9
In what ratio must wheat at ₹24/kg be mixed with wheat at ₹32/kg to get a mixture worth ₹28/kg?
-
Q.10
A vessel contains 40 litres of pure milk. 10 litres are withdrawn and replaced with water (a single operation). Find the ratio of milk to water in the resulting mixture.
-
Q.11
A mixture of 45 litres contains milk and water in the ratio 4 : 1. How much water must be added to make the ratio 2 : 1?
-
Q.12
A shopkeeper mixes 15 kg of sugar costing ₹30/kg with 25 kg of sugar costing ₹42/kg. Find the average price of the mixture.
Show answer
Answer: ₹37.50/kg. Total cost = 450 + 1,050 = 1,500; total qty = 40; 1,500/40.
-
Q.13
A vessel has 50 litres of pure milk. 10 litres are withdrawn and replaced with water, and this is repeated once more. Find the milk left after both operations.
How these questions were made
Written by Mahesh Srivastava, Founder of Pariksha Saathi. Published: 2026-10-03.