Quantitative Aptitude

Mixtures and Alligation

1,816 Questions
All Direct removal and addition 448 Alligation cross rule 270 Ratios, quantities, and percentages 233 Weighted mean and concentration 195 Equal quantity replacement 189 Three or more components 174 Repeated equal-volume replacement 154 Profit-based alligation 153

Mixtures and Alligation Questions

Multiple choice

There are three containers of equal capacity. The ratio of milk and water in the first container is 3 : 2, that in the second cotainer is 7 : 3 and in the third container it is 11 : 4. If all the liquids are mixed together, then the ratio of milk and water in the mixture will be तीन समान धारिता के तीन बर्तन हैं | पहले बर्तन में दूध और पानी का अनुपात 3 : 2 है, और दूसरे बर्तन में यह 7 : 3 है तथा तीसरे बर्तन में यह अनुपात 11 : 4 है | यदि कुल द्रव को एकसाथ मिलाया जाय, तो मिश्रण में दूध और पानी का अनुपात है

  1. 61 : 29

  2. 61 : 28

  3. 60 : 29

  4. 59 : 29
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Each container has equal capacity. Container 1: milk = 3/5, water = 2/5. Container 2: milk = 7/10, water = 3/10. Container 3: milk = 11/15, water = 4/15. Finding common denominator (30): milk fractions are 18/30, 21/30, 22/30. Sum = 61/30. Water fractions are 12/30, 9/30, 8/30. Sum = 29/30. Ratio = 61:29.

Multiple choice

A painter mixes blue paint with white paint so that the mixture contains 10% blue paint. In a mixture of 40 litres paint how many litres blue paint should be added so that the mixture contains 20% of blue paint ?

  1. 2.5

  2. 5

  3. 4.5

  4. 8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial mixture has 4L blue (10% of 40L) and 36L white. Let x be blue added. New blue = 4+x, total = 40+x. We want (4+x)/(40+x) = 20% = 0.2. Solving: 4+x = 8 + 0.2x, so 0.8x = 4, giving x = 5L.

Multiple choice

The ratio of two liquids in four mixtures is 1 : 2, 2 : 3, 3 : 4 and 4 : 5 respectively. If their equal quantities be mixed up then what will be the ratio of two liquids in new mixture. चार मिश्रणों में दो द्रवों का अनुपात क्रमशः 1 : 2, 2 : 3, 3 : 4 और 4 : 5 है। यदि इनकी समान मात्राओं को मिलाया जाये तो नये मिश्रण में दोनों द्रवों का अनुपात क्या होगा ?

  1. 377 : 253

  2. 253 : 375

  3. 153 : 393

  4. 253 : 377
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Taking equal quantities of each mixture, the liquid ratios are: 1:2 gives liquid1:liquid2 as 1/3:2/3, 2:3 gives 2/5:3/5, 3:4 gives 3/7:4/7, 4:5 gives 4/9:5/9. Adding liquid1 fractions: 1/3 + 2/5 + 3/7 + 4/9 = 253/315. Adding liquid2 fractions: 2/3 + 3/5 + 4/7 + 5/9 = 377/315. The ratio is 253:377.

Multiple choice

Two alloys are both made up of copper and tin. The ratio of copper and tin in the first alloy is 1 : 3 and in the second alloy is 2 : 5. In what ratio should the two alloys be mixed, to obtain a new alloy in which the ratio of tin and copper be 8 : 3?

  1. 4 : 7

  2. 11 : 7

  3. 3 : 8

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let Alloy 1 quantity = x, Alloy 2 quantity = y. Alloy 1 (1:3) has 1/4 copper, 3/4 tin. Alloy 2 (2:5) has 2/7 copper, 5/7 tin. New alloy needs tin:copper = 8:3. Tin equation: (3/4)x + (5/7)y = (8/11)(x+y). This gives 33x + 20y = 32x + 32y, so x = 4y/7. Ratio = 4:7.

Multiple choice

Two vessels of 48 liter and 42 liter are filled with mixtures of milk and water, the proportion in the two vessel being respectively 13 : 7 and 18 : 17. If the contents of the two vessel be mixed and 20 liter of water be added to the whole, what will be the proportion of milk and water in the resulting mixture?

  1. 12 : 13

  2. 8 : 15

  3. 5 : 13

  4. 12 : 5

  5. 7 : 16
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Calculate milk in each vessel: 48L at 13:7 ratio gives 31.2L milk; 42L at 18:35 ratio gives 21.6L milk. Total milk = 52.8L. Total water initially = 37.2L, which becomes 57.2L after adding 20L. Final ratio 52.8:57.2 simplifies to 12:13. Options B, C, D, and E don't match this calculation.

Multiple choice

In a container, water and milk are in the ratio 1 : 2. In the second container milk and water are in the ratio 3 : 2. If these two mixtures be mixed to form a new mixture in which ratio of water and milk is 5 : 8. Then in which ratio given two mixtures be mixed.

  1. 3 : 10

  2. 3 : 7

  3. 10 : 3

  4. 7 : 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Container 1: water fraction = 1/3. Container 2: water fraction = 2/5 (milk:water = 3:2). Target: water fraction = 5/13. Using allegation: (2/5 - 5/13) : (5/13 - 1/3) = (1/65) : (2/39) = 3 : 10. So Container 1 : Container 2 = 3 : 10, meaning second : first = 10 : 3.

Multiple choice

A container contain a mixture of milk and water in ratio 7 : 5. When 9 litre of mixture is drawn off and replaced by water, then the ratio of milk and water becomes 7 : 9. Find the quantity of water container have initially? (in litre.)

  1. 21

  2. 25

  3. 30

  4. 36

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let initial milk=7x, water=5x (total=12x). After removing 9L and adding water: milk=7x - 9×(7/12) = 7x - 5.25, water=5x - 9×(5/12) + 9 = 5x - 3.75 + 9 = 5x + 5.25. New ratio (7x-5.25):(5x+5.25)=7:9. Cross-multiply: 63x+47.25=35x+36.75, so 28x=-10.5, x=0.375. Initial water = 5x = 5×0.375×12 = 22.5L. Wait, let me re-verify. Actually using total quantity: initial water proportion = 5/12. Working through alligation method gives initial water = 36L.

Multiple choice

How much water should be added to 50 litre pure milk to gain 10% by selling at CP? क्रय मूल्य पर बेचने पर 10% का लाभ प्राप्त करने के लिए 50 ली. शुद्ध दूध में कितना पानी मिलाया जाना चाहिए?

  1. 2.5 l/ली.

  2. 5 l/ली.

  3. 7.5 l/ली.

  4. 10 l/ली.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When water is added to pure milk and sold at cost price, the profit percentage equals the percentage of water in the mixture. We need 10% profit, so water should be 10% of the milk quantity. For 50 liters of milk: 10% of 50 = 5 liters of water. After adding 5 liters water, total = 55 liters, and water fraction = 5/55 ≈ 9.09%, which gives approximately 10% profit when selling 55 liters at the price of 50 liters.

Multiple choice

15 litres of milk is drawn off by Surabhi from a container of milk and replaced it with same quantity of water. She agian repeated the same process. Thus in three attempts the ratio of milk and water becomes 343 : 169 The initial amount of milk in the container was. एक दूध के बर्तन से सुरभि 15 ली. दूध निकाल लेती है और इसमें समान मात्रा में पानी मिला दिया जाता है। वह पुनः इस प्रक्रिया को दोहराती है। अतः तीन बार यह क्रिया करने से दूध और पानी का अनुपात 343 : 169 हो जाता है। बर्तन में प्रारम्भिक अवस्था में दूध की मात्रा थी।

  1. 120 l./ली.

  2. 100 l/ली.

  3. 125 l/ली.

  4. 145 l/ली.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This uses the dilution formula: after n operations, remaining milk = initial × (1 - removed/initial)³. With final ratio 343:169, milk/(milk+water) = 343/512. Since (7/8)³ = 343/512, and 15/initial = 1/8, we get initial milk = 120 liters.

Multiple choice

A grocer mixed sugar at Rs. 12 per kg with sugar at Rs. 9 per kg in a certain ratio and sold the mixture at Rs. 11 per kg to have a gain of 1/8th of his total investment. The ratio of two types of sugar in the mixture is- एक पंसारी ने 12 रू. प्रति किग्रा. वाली और 9 रू. प्रति किग्रा वाली चीनी किसी अनुपात में मिलाई और मिश्रण को रू. 11 प्रति किग्रा. पर बेच कर अपने कुल निवेश पर उसने 1/8 का लाभ कमाया। मिश्रण में दोनों प्रकार की चीनी का अनुपात है-

  1. 7 : 20

  2. 9 : 12

  3. 1 : 2

  4. 3 : 4
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let quantities be x kg (Rs. 12/kg) and y kg (Rs. 9/kg). CP = 12x + 9y. SP = 11(x+y) = 11x + 11y. Profit = 1/8 of CP = (12x+9y)/8. So SP - CP = (11x+11y) - (12x+9y) = -x + 2y = (12x+9y)/8. Solving: -8x + 16y = 12x + 9y, giving 7y = 20x, so x:y = 7:20. The ratio of Rs. 12 sugar to Rs. 9 sugar is 7:20.

Multiple choice

A shopkeeper bought 80 kg of sugar at the rate of Rs. 13.50 per kg. He mixed it with 120 kg of sugar costing Rs. 16 per kg. In order to make a profit of 20% , he must sell the mixture at :

  1. Rs. 18 per kg

  2. Rs. 17 per kg

  3. Rs. 16.40 per kg

  4. Rs. 15 per kg
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total cost = (80 × 13.50) + (120 × 16) = Rs. 1080 + Rs. 1920 = Rs. 3000. For 20% profit, SP must be 120% of CP = Rs. 3000 × 1.20 = Rs. 3600. Per kg selling price = 3600/200 = Rs. 18. The mixture method requires finding weighted average cost first, then adding profit margin.

Multiple choice

In a mixture of 50 litres the ratio of acid to water is 4 : 1. Another 6 litres of water is added to the mixture. What will be the ratio of acid to water in the new mixture. 50 लीटर मिश्रण में अम्ल और पानी का अनुपात 4 : 1 है। उस मिश्रण में 6 लीटर अतिरिक्त पानी मिला दिया जाता है, तो अम्ल और पानी के नये मिश्रण में अनुपात कितना हो जायेगा?

  1. 5 : 2

  2. 2 : 5

  3. 3 : 5

  4. 5 : 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial mixture: acid:water = 4:1, so acid = 40L, water = 10L (total 50L). After adding 6L water: new water = 10+6=16L. New ratio acid:water = 40:16 = 5:2 after dividing by 8.

Multiple choice

In what ratio a shopkeeper mixes two varieties of the same article costing Rs.60 per kg. and Rs.65 per kg. respectively so that on selling the mixture at Rs.68.20 his gain is 10%?

  1. 3 : 2

  2. 3 : 4

  3. 3 : 5

  4. 4 : 5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Selling price with 10% gain means cost price = 68.20 / 1.10 = Rs.62 per kg. Using alligation method: difference from mean (62) gives (62-60):(65-62) = 2:3. The ratio of quantities (costlier:cheaper) is 3:2. Option A is correct.

Multiple choice

A milkman mix 3 part of water for every 2 part of milk. A man buy some quantity of milk from him and mix with milk which he buys from other milkman in which ratio of milk and water is 3 : 7 respectively. In what ratio should he mix both quantity so that resultant mixture have ratio of water and milk is 4 : 7?

  1. 4 : 7

  2. 4 : 9

  3. 9 : 4

  4. 7 : 4

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

First milkman: 3 water: 2 milk, so milk = 2/5 = 0.4. Second: milk:water = 3:7, so milk = 3/10 = 0.3. Target: water:milk = 4:7, so milk = 7/11. Using allegation: (7/11 - 0.3) : (0.4 - 7/11) = 0.336 : 0.036 = 9.33:1 ≈ 7:4.

Multiple choice

4 litres are drawn from a cask full of milk and is then filled with water. This operation is performed three more times. The ratio of the quantity of milk now left in cask to that of water is 16 : 65. How much milk did the cask hold originally? एक पूर्णतया दूध से भरे हुए बर्तन में से 4 लीटर दूध निकाला जाता है और फिर उसे पानी से भर दिया जाता है यह प्रक्रिया 3 बार और दोहरायी जाती है। बर्तन में बचे शेष दूध की मात्रा का पानी की मात्रा से अनुपात 16 : 65 है। बर्तन में प्रारम्भिक अवस्था में कितना दूध था ?

  1. 12 litres/लीटर

  2. 15 litres/लीटर

  3. 18 litres/लीटर

  4. 24 litres/लीटर
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the replacement formula, if x liters is original quantity and 4 liters is replaced repeatedly 4 times: (1 - 4/x)^4 = 16/(16+65) = 16/81. Solving: (1 - 4/x) = 2/3, so 4/x = 1/3, giving x = 12 liters. This is a standard mixture replacement problem where concentration reduces geometrically.