Alligation or Mixture – Aptitude Questions and Answers

Mixture and allegation are important concepts in quantitative aptitude used to determine the ratio and cost of sale for a mixture made up of two or more materials.

Prerequisite: Mixture and Alligation

Aptitude Questions on Mixture and Alligation

Q1: From a vessel of 20 liters of pure milk, 1 liter is taken out and replaced with water, so as to keep the volume constant at 20 liters. This process is repeated 5 times. Find the percentage of pure milk left in the vessel after 5 replacements. 

Solution: 

Here, we need to apply the formula [1 – (R / P)] ⁿ

P = Initial quantity of pure element = 20 liters

R = Quantity replaced every time = 1 liter (volume removed and replaced each time)

n = Number of replacements = 5

So, the quantity of pure milk after 5 replacements = [1 – (1 / 20)]⁵

Quantity of pure milk after 5 replacements (0.95)⁵ = 0.7737809375

Therefore, percentage of pure milk left in the vessel after 5 replacements = (0.7737809375) x 100 = 77.378 %   

Q2: A dishonest shopkeeper mixed cheaper quality rice, priced at Rs. 10 / KG with good quality rice, priced at Rs. 25 / KG, and sold the mixture at Rs. 15 / KG. Find the ratio in which he mixes the two qualities of rice. 

Solution:  

Thus, the ratio of quantities of cheaper and good quality rice = 10: 5 = 2: 1

3. A grocer mixes two varieties of rice costing $15 per kg and $20 per kg in the ratio 2:3. What is the price per kg of the resulting mixture?

Solution:

Using the alligation formula:

Mean Price = [Tex]\frac{(15 \times 2) + (20 \times 3)}{2 + 3} = \frac{30 + 60}{5} = \frac{90}{5}[/Tex] = 18

Therefore, the price per kg of the mixture is $18.

4. A vessel contains 60 liters of milk. 12 liters of milk are taken out and replaced with water. If this process is repeated once more, how much milk is now in the vessel?

Solution:

First Removal: Milk left after first replacement = [Tex]60 \times \left(1 – \frac{12}{60}\right) = 60 \times \frac{48}{60}[/Tex] = 48 Litres

Second Removal: Milk left after second replacement = [Tex]48 \times \left(1 – \frac{12}{60}\right) = 48 \times \frac{48}{60}[/Tex] = 38.4 liters.

Therefore, the milk remaining in the vessel is 38.4 liters.

5. How much water must be added to 40 liters of a 20% alcohol solution to make it a 10% alcohol solution?

Solution:

20% of 40 liters = [Tex]\frac{20}{100} \times 40[/Tex] = 8 liters.

Now, the total solution = 40 + 𝑥 liters.

New concentration of alcohol:

[Tex]\frac{8}{40 + x} \times 100[/Tex] = 10

Solve for 𝑥: 8 = 0.1 × (40 + 𝑥) ⇒ 8 = 4 + 0.1𝑥 ⇒ 𝑥 = 40 liters.

So, 40 liters of water must be added.

6. A 20-liter mixture contains milk and water in the ratio 3:1. How much water must be added to make the ratio 1:1?

Solution:

Amount of milk in the mixture: [Tex]\frac{3}{4} \times 20[/Tex] = 15 liters.

Amount of water in the mixture: 20 – 15 = 5 liters.

Let 𝒙 liters of water be added to make the ratio 1:1

Set up the equation: [Tex]\frac{15}{5 + x} = 1 \Rightarrow 15 = 5 + x \Rightarrow x[/Tex] = 10

Therefore, 10 liters of water must be added.

Practice Questions on Alligation or Mixture

1. A shopkeeper mixes two varieties of rice costing ₹50/kg and ₹40/kg. In what ratio should they be mixed to get a mixture worth ₹44/kg?

2. 20 liters of a 40% alcohol solution is mixed with x liters of 80% alcohol solution to get a 50% alcohol solution. Find x.

3. Tea worth ₹300/kg mixed with tea worth ₹180/kg in the ratio 2:3. What is the price of the mixture per kg?

4. If 6 liters of water is added to 24 liters of milk costing ₹40/liter, what is the cost per liter of the mixture?

5. Two alloys A and B contain gold and copper in ratios 3:2 and 4:5 respectively. In what ratio should they be mixed to get an alloy containing gold and copper in ratio 7:5?

6. A vessel contains a mixture of milk and water in ratio 4:1. If 10 liters of water is added, the ratio becomes 4:3. Find the initial quantity of mixture.

7. A trader mixes three varieties of pulses costing ₹60/kg, ₹75/kg, and ₹90/kg to get a mixture worth ₹72/kg. If quantities of first two varieties are equal, find the ratio of mixture.

8. In what ratio should sugar solutions of 20% and 50% be mixed to get a 40% solution?

9. A milk vendor has two varieties of milk with fat content 4% and 8%. How many liters of each should be mixed to get 50 liters of milk with 5% fat content?

10. A jar contains a mixture of acid and water in ratio 2:3. When 5 liters of water is added, the ratio becomes 2:4. Find the initial quantity of acid in the mixture.

kartik

Follow

Improve

Article Tags :

• Placements
• QA - Placements