Hello Aspirants. Welcome to Online Quantitative Aptitude section in AffairsCloud.com. Here we are given some** Mixture and Alligations** problems that is important for competitive exams. We have included Some questions that are repeatedly asked in exams !!

Questions Penned by Yogit

**A man buys milk at the rate of 5 rupees per litre and mixes it with water. By selling the mixture at Rs 4 a litre he gains 25 percent. How much water did each litre of the mixture contain?**

a) 9/25

b) 11/25

c) 16/25

d) 19/25

e) None of these

Answer –**a) 9/25**

**Explanation :**

By rule of allegation

Ratio of water: milk = 9:16, so in one litre water will be = 9/25

**A mixture containing milk and water in the ratio 3:2 and another mixture contains them in the ratio 4:5. How many litres of the later must be mixed with 3 litres of the former so that the resulting mixture may contain equal quantities of milk and water?**

a) 3.3/4 litre

b) 4.1/2 litre

c) 5.2/3 litre

d) 5.2/5 litre

e) None of these

Answer –**d) 5.2/5 litre**

**Explanation :**

milk = 3*3/5 = 9/5 litre and water = 3*2/5 = 6/5 litre (in first mixture)

milk = 4k/9 and water = 5k/9 litres in second mixture, so

9/5 + 4k/9 = 6/5 + 5k/9, we get k = 27/5 litre

**Two vessels contain milk and water in the ratio of 7:3 and 2:3 respectively. Find the ratio in which the contents of both the vessels must be mixed to get a new mixture containing milk and water in the ratio 3:2.**

a) 2:1

b) 2:3

c) 3:1

d) 3:5

e) None of these

Answer –**a) 2:1**

**Explanation :**

let the ratio be k:1

then in first mixture, milk = 7k/10 and water = 3k/10

and in second mixture, milk = 2/5 and water = 3/5

[7k/10 + 2/5]/[3k/10 3/5] = 3/2

K = 2, so ratio will be 2:1

**In 80 litre mixture of milk and water, water content is 40 percent. The trader gives 20 litre of the mixture to the customer and adds 20 litres of water to the mixture. What is the final ratio of milk and water in the mixture?**

a) 9:13

b) 9:11

c) 11:9

d) 12:7

e) None of these

Answer –**b) 9:11**

**Explanation :**

milk = 48 and water = 32 litre initially

then milk = 48 – 20*3/5 = 36 and water = 32 – 20*2/5 + 20 = 44

so ratio = 9:11

**70 litres of a mixture of milk and water contains 20% water. How much water should be added so that the mixture has 28% water?**

a) 50/9 litre

b) 60/9 litre

c) 70/9 litre

d) 100/9 litre

e) None of these

Answer –**c) 70/9 litre**

**Explanation :**

milk = 56 litre and water = 14 litre. Let x litre of water is added the,

(14 + x)/(70 + x) = 28/100

**Rice worth Rs. 110 per kg and Rs. 95 per kg are mixed with a third variety in the ratio 1:1:2. If the mixture is worth Rs. 115 per kg, the price of the third variety per kg will be**

a) 117.5

b) 127.5

c) 137.5

d) 147.5

e) None of these

Answer –**b) 127.5**

**Explanation :**

First two types of rice are mixed in 1:1 so total cost for 2 kg of rice is 205, so average price = 102.5

So, x – 115 = 12.5, x = 127.5

**A trader has 60 kg of pulses, one part of which is sold at 8% profit and the rest is sold at 14% profit. He gains 12% on whole. What is the quantity sold at 14% profit?**

a) 20kg

b) 30kg

c) 40kg

d) 50kg

e) None of these

Answer –**c) 40kg**

**Explanation :**

So ratio will be 1:2, so quantity sold at 14% profit = 2/3*60 = 40kg

**Two cans of 60 and 80 litres are filled with the mixtures of milk and water. The proportion of milk and water in the cans being 5:7 and 9:7 respectively. If the contents of the two cans are mixed and 30 litres of the water is added to the whole, then find the ratio of milk and water in the final mixture?**

a) 7:9

b) 7:10

c) 8:11

d) 9:7

e) None of these

Answer –**b) 7:10**

**Explanation :**

milk = 60*5/12 = 25 and water = 60*7/12 = 35

milk = 80*9/16 = 45 and water = 80*7/16 = 35

milk = 70 and water = 70 + 30 = 100

**There are three vessels each of 20 litre capacity is filled with the mixture of milk and water. The ratio of milk and water are 2:3, 3:4 and 4:5 respectively. All the vessels are emptied into fourth vessel, then find the ratio of milk and water in the final mixture.**

a) 401/543

b) 401/544

c) 401/545

d) 401/546

e) None of these

Answer –**b) 401/544**

**Explanation :**

Milk = 2/5 + 3/7 + 4/9 and water = 3/5 + 4/7 + 5/9

so ratio will be 401/544

**In two alloys copper and zinc are in the ratio of 1:4 and 3:1 respectively. 20 kg of first alloy and 32 kg of second alloy and some pure zinc are melted together. An alloy is obtained in which the ratio of copper and zinc was 3:5. Find the quantity of zinc melted.**

a) 65/3 kg

b) 67/3 kg

c) 68/3 kg

d) 71/3 kg

e) None of these

Answer –**c) 68/3 kg**

**Explanation :**

Copper = 1/5*20 + 3/4*32 = 28kg

zinc = 4/5*20 + 1/4*32 = 24kg

now x kg of zinc is added, so [28/24 + x] = 3/5. X = 68/3 kg

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