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

In 40 litres of milk and water the ratio of milk to water is (7 : 1). To get a new mixture containing milk and water in the ratio (3 : 1), the quantity of water that should be added to the mixture?

  1. 6

  2. 6.5

  3. 6.67

  4. 13.5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In 40 liters with milk:water ratio 7:1, milk = 35 liters, water = 5 liters. Let x be water added. New ratio is 3:1, so 35/(5+x) = 3/1. This gives 35 = 15 + 3x, so 3x = 20, and x = 6.67 liters approximately.

Multiple choice

A 136 m.l. mixture with 25% alcohol content is mixed with 64 ml of water. What is the percentage of alcohol in the new solution? एक 136 मिलीलीटर मिश्रण में 25% अल्कोहल है ,जिसमें 64 मिलीलीटर पानी मिलाया जाता है, तो नए विलयन में अल्कोहल कितना प्रतिशत है?

  1. 34%

  2. 45%

  3. 17%

  4. 18%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Alcohol in original mixture = 25% of 136 ml = 34 ml. Total volume after adding water = 136 + 64 = 200 ml. Percentage of alcohol = (34/200) × 100 = 17%. When water is added to a solution, the amount of solute remains constant while total volume increases, decreasing concentration.

Multiple choice

A vessel contain a mixture of sprit and water in ratio 16 : 25 respectively. 54 litre of water added to mixture then ratio of sprit and water become 4 : 7. Then find the initial quantity of mixture. एक बर्तन में स्प्रिट और जल का अनुपात 16 : 25 है। यदि 54 ली. जल और मिला दिया जाता है। तो यह अनुपात 4 : 7 हो जाता है तो शुरू में मिश्रण की मात्रा ज्ञात कीजिए।

  1. 730

  2. 450

  3. 738

  4. 816
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let spirit = 16x, water = 25x. After adding 54L water: 16x/(25x+54) = 4/7. Cross-multiply: 112x = 100x + 216. So 12x = 216, x = 18. Initial mixture = 41x = 41×18 = 738L.

Multiple choice

A container fully filled with water and milk is in the ratio 2 : 3. 10 litres mixture is replaced by water then ratio of water and milk becomes 13 : 12. Then find how many litres of milk was contained in container initially. एक जार पूरी तरह से पानी और दूध के मिश्रण से भरा है। 10 ली. मिश्रण निकालकर पानी से प्रतिस्थापित कर दिया जाता है तो पानी और दूध का अनुपात 13 : 12 हो जाता है। प्रारम्भ में जार में दूध की मात्रा क्या थी ?

  1. 20 l/ली.

  2. 50 l/ली.

  3. 80 l/ली.

  4. 30 l/ली.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let initial water = 2x, milk = 3x. Total = 5x. In 10 litres removed, water removed = 10 × (2x/5x) = 4 litres, milk removed = 6 litres. After replacement: water = 2x - 4 + 10 = 2x + 6, milk = 3x - 6. New ratio (2x + 6) : (3x - 6) = 13 : 12. Cross-multiplying: 12(2x + 6) = 13(3x - 6), giving 24x + 72 = 39x - 78. Solving: 15x = 150, x = 10. Initial milk = 3x = 30 litres.

Multiple choice

The ratio of two liquids in four jar is 1 : 2, 2 : 1, 3 : 1 and 2 : 3 respectively. If the ratio of their quantities in jar is 1 : 2 : 3 : 4. If all jar mixed up then what will be the ratio of two liquids in new mixture.
  1. $269 : 144$
  2. $445 : 331$
  3. $113 : 445$
  4. $331 : 269$

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

Jar ratios (liquid1:liquid2) are 1:2, 2:1, 3:1, 2:3 with quantities in ratio 1:2:3:4. Take quantities as x, 2x, 3x, 4x. Liquid1 total = 1×x + 2×2x + 3×3x + 2×4x = x+4x+9x+8x = 22x. Liquid2 total = 2×x + 1×2x + 1×3x + 3×4x = 2x+2x+3x+12x = 19x. Ratio = 22:19. This doesn't match any option. Let's use different approach: For jar1 with 3 parts (1:2), quantity x means x/3 and 2x/3. Jar2 (2:1) with 2x means 4x/3 and 2x/3. Jar3 (3:1) with 3x means 9x/4 and 3x/4. Jar4 (2:3) with 4x means 8x/5 and 12x/5. Summing: Liquid1 = x/3+4x/3+9x/4+8x/5, Liquid2 = 2x/3+2x/3+3x/4+12x/5. Computing LCM: Liquid1 = (20x+80x+135x+96x)/60 = 331x/60, Liquid2 = (40x+40x+45x+144x)/60 = 269x/60. Ratio = 331:269.

Multiple choice

A vessel contains 120 liters of juice. 20% of this juice is taken out and the same is repeated two more times. Water of amount equal to the juice taken out is mixed with the remaining juice in the vessel. What is the ratio of the juice and the water in the vessel? एक बर्तन में 120 ली. जूस है जिसका 20% जूस बाहर निकाला गया यही प्रक्रिया दो बार और दोहराई गई । बचे हुए जूस में निकाले गए जूस की मात्रा के बराबर पानी की मात्रा मिलाई गई । अब बर्तन में पानी और जूस का अनुपात क्या है ?

  1. 61 : 64

  2. 121 : 141

  3. 32 : 63

  4. 64 : 61
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial juice = 120L. After 1st removal: 120 × 0.8 = 96L juice, water = 24L. After 2nd removal: 96 × 0.8 = 76.8L juice, water = 24 + 19.2 = 43.2L. After 3rd removal: 76.8 × 0.8 = 61.44L juice, water = 43.2 + 15.36 = 58.56L. Ratio = 61.44:58.56 = 64:61.

Multiple choice

In vessel A milk and water is in the ratio 5 : 1 whereas in vessel B milk and water is in the ratio 5 : 3. If the ratio of volume of vessel A and vessel B is in ratio 2 : 3 then what will be the ratio of water and milk when both are mixed together?

  1. 17 : 7

  2. 37 : 12

  3. 12 : 37

  4. 7 : 17

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

Vessel A ratio 5:1 means 5/6 milk, 1/6 water. Vessel B ratio 5:3 means 5/8 milk, 3/8 water. Volume ratio A:B is 2:3. Let A = 60 units, B = 90 units. A has 50 milk + 10 water. B has 56.25 milk + 33.75 water. Combined: 106.25 milk + 43.75 water = 150 total. Water:Milk = 43.75:106.25 = 7:17. Option D is correct.

Multiple choice

The milk and water in two vessels A and B are in the ratio 4 : 3 and 2 : 3 respectively. In what ratio, the liquids in both the vessels be mixed to obtain a new mixture in vessel C containing half milk and half water?

  1. 7 : 5

  2. 5 : 2

  3. 3 : 11

  4. 1 : 2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Use alligation on milk fractions: vessel A has 4/7 milk, vessel B has 2/5 milk. Target is 1/2 milk. Deviations: |4/7 - 1/2| = 1/14, |2/5 - 1/2| = 1/10. Ratio is inverse: 1/14 : 1/10 = 10:14 = 7:5. Mixing A and B in 7:5 gives equal milk and water.

Multiple choice

The proportion of acid and water in three samples is 3 : 2 ,4 : 3 and 5 : 2. A mixture containing equal quantities of all three samples is made. What is the ratio of water and acid in the mixture? तीन मिश्रण में तेजाब और पानी का अनुपात 3: 2, 4: 3 और 5: 2. सभी तीन मिश्रण की बराबर मात्रा को लेकर मिलाया जाता है।नए मिश्रण में पानी और तेजाब का अनुपात क्या होगा ?

  1. 66 : 43

  2. 22 : 13

  3. 11 : 13

  4. 13 : 22
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In equal quantities (say 1 unit each): Acid total = 3+4+5 = 12 parts. Water total = 2+3+2 = 7 parts. But wait - we need the actual quantities. Sample 1: 3:2 means 3/5 acid, 2/5 water. Sample 2: 4:3 means 4/7 acid, 3/7 water. Sample 3: 5:2 means 5/7 acid, 2/7 water. In 3 units total: Acid = 3/5 + 4/7 + 5/7 = 3/5 + 9/7 = (21+45)/35 = 66/35. Water = 2/5 + 3/7 + 2/7 = 2/5 + 5/7 = (14+25)/35 = 39/35. Ratio water:acid = 39:66 = 13:22.

Multiple choice

Two container of equal capacity contain a mixture of milk and water. The ratio of milk and water between 2 : 3 in 1st container and 3 : 4 in 2nd container. Now the mixtures of both containers are poured in a third container. Find the ratio of milk and water in third container. समान क्षमताा के दो बर्तनों में दूध और पानी का मिश्रण क्रमशः 2 : 3 और 3 : 4 के अनुपात में भरा है। दोनो को तीसरे बर्तन में डाल दिया जाता है। तीसरे बर्तन में दूध और पानी का अनुपात ज्ञात कीजिये ।

  1. 29 : 40

  2. 30 : 31

  3. 41 : 29

  4. 29 : 41
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let each container have capacity 35. First container: milk = 2/5 of 35 = 14, water = 3/5 of 35 = 21. Second container: milk = 3/7 of 35 = 15, water = 4/7 of 35 = 20. Total milk = 14 + 15 = 29. Total water = 21 + 20 = 41. Ratio milk:water = 29:41. Key is to use a common denominator or LCM to combine ratios.

Multiple choice

A man purchased 150 kg. of rice at Rs 50 per kg. and mixed it with a 180 kg. of the priced Rs. 75 per kg. At what price (per kg.) should he sell the mixture to make a profit of 21%? एक ब्यक्ति 150 किग्रा. चावल 50 रुपये प्रति किग्राके भाव से खरीदता है और इसे 75 रुपये प्रति किग्रा. चावल के भाव वाले 180 किग्रा. चावल में मिला देता है। 21% का लाभ प्राप्त करने के लिए उसे मिश्रण को किस कीमत पर (प्रति किग्रा.) बेचना चाहिए ?

  1. 73

  2. 79

  3. 97

  4. 77
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total cost price = (150 × 50) + (180 × 75) = 7500 + 13500 = Rs. 21000. Total quantity = 150 + 180 = 330 kg. Cost price per kg = 21000/330 = Rs. 63.64. For 21% profit, selling price = 63.64 × 1.21 = Rs. 77.01. Rounding gives Rs. 77. Option D is correct.