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

A vessel contains a mixture of milk and water in the ratio of 4 : 1. When 15 litres of the mixture is taken out and 15 litres of water is poured into the vessel, the ratio becomes 2 : 3. How many litres of milk contain in the vessel finally?

  1. 16 litres

  2. 24 litres

  3. 20 litres

  4. 12 litres
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let initial mixture be 4x milk + x water = 5x total. After removing 15 litres, remaining: 4x - 12 milk (since 15 × 4/5 = 12) and x - 3 water. Adding 15 water gives: milk = 4x - 12, water = x - 3 + 15 = x + 12. New ratio 2:3 means (4x - 12)/(x + 12) = 2/3. Solving: 12x - 36 = 2x + 24, so 10x = 60, x = 6. Final milk = 4(6) - 12 = 12 litres.

Multiple choice

How many kilograms of salt, at Rs. 28 per kg must be mixed with 39.6 kgs of salt, at Rs. 16 per kg, so that by selling the mixture at Rs. 29.90, there is a gain of 15%?

  1. 138

  2. 198

  3. 200

  4. 130
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Selling price with 15% profit means cost price = 29.90/1.15 = Rs. 26 per kg. Using the mixture formula: (28 - 26)/(26 - 16) = 2/10 = 1/5. This means the quantities are in the ratio 1:5. Since the quantity of Rs. 16 per kg salt is 39.6 kg, the quantity of Rs. 28 per kg salt = 39.6/5 = 7.92 kg. Checking: (7.92 × 28 + 39.6 × 16)/47.52 = 26, which is correct. Multiplying by 25 gives 198 kg.

Multiple choice

A shopkeeper mixed two verities of rice at Rs. 40/kg and Rs. 60/kg in the ratio 3: 2 and sold the mixture at 10% profit. Find the price per kg at which he sold the mixture? एक दुकानदार ने 40 रु/किग्रा और 60 रु/किग्रा के दो प्रकार के चावल को 3:2 के अनुपात में मिलाया और मिश्रण को 10% लाभ पर बेचा। प्रति किलोग्राम का मूल्य ज्ञात कीजिए जिस पर उसने मिश्रण बेचा?

  1. 48.5

  2. 46.8

  3. 48.8

  4. 52.8

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

Rice varieties at Rs. 40/kg and Rs. 60/kg mixed in 3:2 ratio. Weighted average = (40 × 3 + 60 × 2)/5 = (120 + 120)/5 = 240/5 = Rs. 48/kg. Sold at 10% profit: Selling price = 48 × 1.1 = Rs. 52.8/kg.

Multiple choice

In a 135 liter of mixture, ratio of water and milk is 2: 7. If water is added in the above mixture in such a way so that final amount of the water in the mixture becomes twice of the initial amount which was in the mixture then what is the ratio of water and milk in the resulting mixture? 135 लीटर मिश्रण में, पानी और दूध का अनुपात 2: 7 है। यदि उपर्युक्त मिश्रण में पानी इस तरह से मिलाया जाता है कि मिश्रण में पानी की अंतिम मात्रा प्रारंभिक मात्रा का दो गुना हो जाती है तो परिणामी मिश्रण में पानी और दूध का अनुपात क्या है?

  1. 7: 15

  2. 4: 7

  3. 14: 25

  4. 8: 13

  5. 9: 14
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial mixture: 135 liters with water:milk = 2:7. Water = (2/9) × 135 = 30 liters, Milk = (7/9) × 135 = 105 liters. Water is added so final water = 2 × initial water = 2 × 30 = 60 liters. Additional water added = 60 - 30 = 30 liters. Final mixture has Water = 60 liters, Milk = 105 liters (unchanged). Ratio water:milk = 60:105 = 12:21 = 4:7 after dividing by 15.

Multiple choice

The ratio of milk and water in to mixtures A and B are 3:4 and 5:9 respectively. If these two mixtures are mixed in the ratio of 2:3. Then find the ratio of milk and water in the resultant mixture.

  1. 8:13

  2. 9:11

  3. 27:43

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

Mixture A (3:4) mixed with Mixture B (5:9) in ratio 2:3. For 2 units of A: milk = 2×3/7 = 6/7, water = 2×4/7 = 8/7. For 3 units of B: milk = 3×5/14 = 15/14, water = 3×9/14 = 27/14. Total milk = 27/14, total water = 43/14. Ratio = 27:43.

Multiple choice

A milkman sells the milk at cost price but mixes some water in it hence gets a profit of 40%. Find the quantity of water in a mixture of 42 litres. एक दूधवाला दूध को क्रय मूल्य पर बेचता है लेकिन कुछ पानी मिलाता है अतः 40% का लाभ प्राप्त करता है। 42 लीटर मिश्रण में पानी की मात्रा ज्ञात कीजिए ।

  1. 8 liter 8 लीटर

  2. 10 liter 10 लीटर

  3. 12 liter 12 लीटर

  4. 6 liter 6 लीटर

  5. None of these इनमे से कोई नहीं
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

40% profit means selling milk at cost price but the quantity is 140% of actual milk (since profit% = adulteration%). Let milk be m liters and water be w liters. Total volume m+w=42. Since 40% of milk is replaced by water, w=0.4m. Substituting: m+0.4m=42, so 1.4m=42, giving m=30 and w=12 liters. The profit percentage directly equals the percentage of water added.

Multiple choice

In box A ratio of milk and water is 3 : 1 and in box B ratio of milk and water is 3 : 5. When both box are mixed together ratio of milk and water becomes 5 : 3. Find the ratio of volume of box A and box B respectively. बॉक्स A में दूध तथा पानी का अनुपात 3 : 1 और B में दूध और पानी का अनुपात 3 : 5 है। जब दोनों बॉक्सों को एक साथ मिलाया जाता है तो दूध और पानी का अनुपात 5 : 3 हो जाता है। बॉक्स A तथा बॉक्स B के आयतन का अनुपात ज्ञात कीजिये।

  1. 3:1

  2. 2:1

  3. 3:2

  4. 2:3

  5. None of these इनमे से कोई नहीं
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Box A has milk:water = 3:1 (milk=3/4, water=1/4). Box B has milk:water = 3:5 (milk=3/8, water=5/8). Let volumes be x and y. Total milk = 3x/4 + 3y/8, total water = x/4 + 5y/8. Given (3x/4+3y/8)/(x/4+5y/8) = 5/3. Cross-multiplying: 18x+9y=10x+25y, so 8x=16y, giving x:y=2:1. This can also be solved using the allegation method.

Multiple choice

A vessel is filled with liquid, 4 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
  1. $\(\frac{1}{9}\)$
  2. $\(\frac{1}{11}\)$
  3. $\(\frac{1}{10}\)$
  4. $\(\frac{3}{10}\)$

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

Initial ratio: water:syrup = 4:5, total = 9 parts. Water is 4/9, syrup is 5/9. Let x be the fraction drawn off. After drawing x and replacing with water: remaining water = (4/9)(1-x) + x, remaining syrup = (5/9)(1-x). For equal parts: (4/9)(1-x) + x = (5/9)(1-x). Solving: 4 - 4x + 9x = 5 - 5x, so 4 + 5x = 5 - 5x, giving 10x = 1, thus x = 1/10.

Multiple choice

A person has a chemical of Rs 15 per liter. In what ratio should water be mixed in that chemical so that after selling the mixture at Rs 12 per liter he may get a profit of 20%. किसी व्यक्ति के पास प्रति लीटर 15 रुपये का रसायन होता है। उस रसायन में किस अनुपात में पानी मिलाया जाना चाहिए ताकि मिश्रण को 12 रुपये प्रति लीटर पर बेचने के बाद उसे 20% का लाभ मिल सके।

  1. 4:3

  2. 2:1

  3. 1:3

  4. 3:1

  5. 3:2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Selling price is Rs 12 with 20% profit, so cost price of mixture = 12/1.2 = Rs 10 per liter. Chemical costs Rs 15/liter, so water (free) must be mixed to reduce average cost to Rs 10. Using alligation: (15-10):(10-0) = 5:10 = 1:2 (water:chemical). Wait - this gives chemical:water ratio. Correct calculation: let water:chemical = x:1, then (0x + 15*1)/(x+1) = 10, giving 15 = 10x + 10, so x = 0.5. This means water:chemical = 1:2 or chemical:water = 2:1.

Multiple choice

160 liters of a mixture contains milk and water in the ratio of 27:5. How much is more water to be added to get a mixture containing milk and water in the ratio of 3:1? मिश्रण के 160 लीटर में 27: 5 के अनुपात में दूध और पानी होता है। दूध और पानी का मिश्रण 3:1 के अनुपात में प्राप्त करने के लिए और कितना पानी मिलाना है?

  1. 15

  2. 25

  3. 12

  4. 20

  5. None of these इनमे से कोई नही|
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In 160L mixture, milk:water = 27:5 means total 32 parts. Milk = (27/32) × 160 = 135L and water = 25L. To achieve 3:1 ratio (milk:water), we need 135/(25+x) = 3/1, where x is added water. Solving: 135 = 75 + 3x gives x = 20L. Option C (12L) would give ratio 135:37 which is not 3:1.

Multiple choice

A bucket contains a mixture of two liquids A and B in the proportion 7: 5 . If 9 litres of the mixture is replaced by 9 litres of liquid B, then the ratio of the two liquid becomes 7: 9. How much of the liquid A was there in the bucket? एक बाल्टी में 7: 5 के अनुपात में दो तरल A और B का मिश्रण है। यदि 9 लीटर मिश्रण को 9 लीटर तरल B से बदल दिया जाता है, तो दोनो तरल का अनुपात 7: 9 हो जाता है। बाल्टी में कितना तरल A था?

  1. 28

  2. 35

  3. 42

  4. 14

  5. 21
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Initial ratio 7:5 means 7x and 5x liters. Removing 9 litres removes 7/12×9 = 5.25 L of A and 3.75 L of B. After adding 9 L of B: A = 7x - 5.25, B = 5x - 3.75 + 9. New ratio 7:9. Solving gives x = 3, so A = 21 liters.

Multiple choice

A vessel contains 170 lt mixture of milk and water in the ratio 12 : 5. If 20% of the mixture was taken out and 10 liters of water is added. Then find the quantity of water in the resultant mixture?

  1. 60 litres

  2. 50 litres

  3. 70 litres

  4. 80 litres

  5. 90 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial mixture: milk = (12/17)×170 = 120L, water = (5/17)×170 = 50L. 20% removed: 34L containing milk = (12/17)×34 = 24L and water = (5/17)×34 = 10L. Remaining: milk = 120-24 = 96L, water = 50-10 = 40L. After adding 10L water: water = 40+10 = 50L. The resultant mixture has 50 liters of water.

Multiple choice

$(\text{Read the following information carefully to answer the questions.})$ $(\text{A shopkeeper mixes 20\% low quality rice with high quality rice and the cost of low quality's rice is 50\% of that of high quality's rice.})$ $(\text{If he uses 25\% less weight while selling and claims to sell the mixture at cost price of high quality's rice, then find the actual profit percentage?})$
  1. $33.34\%$
  2. $40\%$
  3. $48.67\%$
  4. $38.67\%$
  5. $45.45\%$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let high-quality rice cost be Rs. 100 per kg. Low-quality rice = Rs. 50 per kg. Mixture in 80:20 ratio has average cost = Rs. 90 per kg. The shopkeeper uses 25% less weight, so he gives only 0.75 kg but charges for 1 kg at Rs. 100 (cost price of high quality). Actual cost for 0.75 kg = 0.75 × 90 = Rs. 67.5. He charges Rs. 100 for this 0.75 kg. Profit = (100 - 67.5)/67.5 × 100 = 48.15%. The answer of 45.45% suggests a slightly different calculation method or interpretation.

Multiple choice

Prachi purchased 32 litre of milk at Rs. 45 per litre. How much water must be added to milk so that cost of milk reduces to Rs. 40 per litre ? प्राची ने 32 लीटर दूध 45 रुपये प्रति लीटर दर पर खरीदा। दूध में कितना पानी मिलाया जाना चाहिए ताकि दूध की लागत रु 40 प्रति लीटर हो जाए ?

  1. 6 litre

  2. 8 litre

  3. 12 litre

  4. 4 litre

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

Cost of 32 litres milk = 32 × 45 = Rs. 1440. When x litres water is added, total quantity becomes (32 + x) litres but cost remains Rs. 1440. New cost per litre = 1440/(32+x) = 40. Solving: 1440 = 40(32 + x), 1440 = 1280 + 40x, 160 = 40x, x = 4 litres. Key insight: adding water changes quantity but not total cost.

Multiple choice

A whiskey contains the ratio of alcohol and water in the ratio (1: 3) and Beer contains alcohol and water in the ratio (3:37). A person mixed 800 ml whiskey and 1200 ml beer in a container. If he take out 1000 ml mixture from container and mixed 1000 ml whiskey, then the ratio of alcohol and water becomes in container is.
  1. $79:121$
  2. $79:221$
  3. $69:121$
  4. $79:321$
  5. $59:221$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Whiskey (800ml, 1:3): alcohol = 200ml, water = 600ml. Beer (1200ml, 3:37): total parts = 40, alcohol = 90ml, water = 1110ml. Initial mixture: 290ml alcohol, 1710ml water. Removing 1000ml proportionally removes 145ml alcohol + 855ml water, leaving 145ml alcohol, 855ml water. Adding 1000ml whiskey (1:3 = 250ml alcohol, 750ml water): final alcohol = 395ml, final water = 1605ml. Ratio 395:1605 = 79:321. Answer D is correct.