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 person has two varieties of oil costing 72 Rs. / litre and 120 Rs./litre. In what ratio he should mix these two varieties so that by selling mixture at 101.25 Rs./litre he may get a profit of 12.5% ? एक व्यक्ति के पास दो प्रकार के तेल हैं जिनका मूल्य 72 रू. /लीटर और 120 रू./लीटर है। उसे इन दो किस्मों को किस अनुपात में मिलाना चाहिये ताकि मिश्रण को 101.25 रू./लीटर में बेचेने पर उसे 12.5% का लाभ प्राप्त हो?

  1. 5 : 4

  2. 5 : 3

  3. 3 : 1

  4. 4 : 1

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

Selling at 12.5% profit means cost price of mixture = 101.25/1.125 = 90 Rs/L. Using allegation: (120 - 90) : (90 - 72) = 30 : 18 = 5 : 3. Mix in ratio 5:3 (costlier:cheaper). Option B (5:3) is correct.

Multiple choice

In mixture of 40 litres of milk and water contains 10% water. How much water must be added to make water 20% in the new mixture? 40 लीटर दूध और पानी के मिश्रण में 10% पानी है। मिश्रण में पानी की मात्रा क्या मिला दी जाये कि पानी की मात्रा 20% हो जाये?

  1. 6 litres 6 लीटर

  2. 8 litres 8 लीटर

  3. 10 litres 10 लीटर

  4. 5 litres 5 लीटर

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

In 40 litres, water is 10%, so water = 4 litres, milk = 36 litres. Let x litres of water be added. New water = 4 + x, new total = 40 + x. We want (4 + x) / (40 + x) = 20% = 0.2. So 4 + x = 0.2(40 + x) = 8 + 0.2x. Therefore x - 0.2x = 8 - 4, so 0.8x = 4, giving x = 5 litres.

Multiple choice

In what ratio must water be mixed with milk costing Rs. 12 per liter to obtain a mixture worth of Rs. 8 per liter? 12 रुपये प्रति लीटर के दूध व पानी को किस अनुपात में मिलाया जाये कि मिश्रण की कीमत 8 रु प्रति लीटर हो जाए ?

  1. 2:1

  2. 3:1

  3. 3:2

  4. 2:3

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

Using alligation: water costs Rs. 0/liter, milk costs Rs. 12/liter, mixture costs Rs. 8/liter. By alligation rule, ratio of water to milk = (12-8):(8-0) = 4:8 = 1:2, so water:milk = 1:2 or milk:water = 2:1.

Multiple choice

Two container A and B contains mixture of milk and water in the ratio of 5:7 and 5:1 respectively. If 37.5L mixture from container A and 25L mixture from container B are taken out and mixed in container C then what will be the ratio of water and milk in container C? दो बर्तन Aऔर B में क्रमशः 5: 7 और 5: 1 के अनुपात में दूध और पानी का मिश्रण है।यदि बर्तन A से 37.5L मिश्रण और बर्तन B से 25L मिश्रण लेकर बर्तन C में मिलाया जाता है तो बर्तन C में पानी और दूध का अनुपात क्या होगा?

  1. 7:5

  2. 2:3

  3. 3:2

  4. 3:4

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

Container A has milk:water = 5:7, so in 37.5L: milk = 5/12 × 37.5 = 15.625L, water = 7/12 × 37.5 = 21.875L. Container B has milk:water = 5:1, so in 25L: milk = 5/6 × 25 = 20.833L, water = 1/6 × 25 = 4.167L. Total water in C = 21.875 + 4.167 = 26.042L. Total milk in C = 15.625 + 20.833 = 36.458L. Ratio water:milk = 26.042:36.458 = 5:7 (approximately 0.714). This ratio is not listed in options A-D, so E is correct.

Multiple choice

In two containers the ratio of milk and water are 7:4 and 6:5. If the solution of both containers are mixed in the ratio of 1:1 in the third container, then find ratio of milk and water in the third container? दो कंटेनरों में दूध और पानी का अनुपात 7: 4 और 6: 5 है। यदि दोनों कंटेनरों का घोल तीसरे कंटेनर में 1: 1 के अनुपात में मिलाया जाता है, तो तीसरे कंटेनर में दूध और पानी का अनुपात ज्ञात करें?

  1. 9:13

  2. 3:4

  3. 4:5

  4. 13:9

  5. Can’t be determined निर्धारित नही किया जा सकता
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Container 1 has milk:water = 7:4 (total 11 parts). Container 2 has 6:5 (total 11 parts). Taking equal quantities means we combine 7+6=13 parts milk and 4+5=9 parts water. Final ratio is 13:9. Option A reverses this ratio, and Option B would give 12:16.

Multiple choice

A person has a chemical of Rs. 50 per litre. In what ratio should water be mixed in that chemical, so that after selling the mixture at Rs. 40 per litre he may get a profit of 25%? एक व्यक्ति के पास 50 रुपये प्रति लीटर का रसायन है। उस रसायन में किस अनुपात में पानी मिलाया जाना चाहिए, ताकि मिश्रण को 40 रुपये प्रति लीटर पर बेचने के बाद उसे 25% का लाभ मिल सके?

  1. 9: 15

  2. 10: 13

  3. 16: 9

  4. 15: 22

  5. 21: 17
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To earn 25% profit selling at Rs. 40/liter, the cost price must be 40/1.25 = Rs. 32/liter. Using alligation between water (Rs. 0/liter) and chemical (Rs. 50/liter): (50-32):(32-0) = 18:32 = 9:16. The ratio of chemical to water is 16:9.

Multiple choice

A chemist mixes two liquids 1 and 2. One litre of liquid 1 weighs 1 kg and one litre of liquid 2 weighs 800 gm. If half litre of the mixture weighs 480 gm, then find the percentage of liquid 1 in the mixture? एक रसायनज्ञ दो तरल पदार्थ A तथा B को मिलता है। यदि 1 लीटर A का भार 1 किलो जबकि B का भार 800 ग्राम है। यदि आधा लीटर मिश्रण का भर 480 ग्राम है, तो मिश्रण में तरल A कितने प्रतिशत है ?

  1. 85%

  2. 70%

  3. 75%

  4. 80%

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

1 L of mix = 960 g (since 0.5 L = 480 g). Let fraction of liquid 1 be x, then x(1000) + (1-x)(800) = 960. Solving: 200x = 160, x = 0.8 = 80%. Weighted average principle.

Multiple choice

In what ratio must a shopkeeper have to mix the two varieties of rice costing Rs 28 and Rs 40 per kg respectively so as to get a mixture worth Rs 36 per kg ? किस अनुपात में दुकानदार को चावल की दो किस्मों को क्रमशः 28 रुपये और 40 रुपये प्रति किलो के हिसाब से मिलाना होगा , ताकि 36 रुपये प्रति किलो के हिसाब से मिल सके ?

  1. 4 : 7

  2. 2 : 3

  3. 1 : 2

  4. 5 : 8

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

Using allegation method: Rice at Rs.28 is Rs.8 below the target Rs.36, while rice at Rs.40 is Rs.4 above. The ratio is the inverse of these differences: (40-36):(36-28) = 4:8 = 1:2. This means for every 1 kg of Rs.40 rice, mix 2 kg of Rs.28 rice.

Multiple choice

In a mixture of milk and water, milk and water are in a ratio of 4:3. Another mixture with same ingredients, the ratio of milk and water is 5:2. If both the mixture are mixed in the ratio of 5:6, then find the % of water in the resultant mixture (approximately).

  1. 39

  2. 35

  3. 54

  4. 46
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Mixture 1 has 3/7 water, Mixture 2 has 2/7 water. Mixed in ratio 5:6. Using weighted average: Water% = (5×3/7 + 6×2/7)/(5+6) = (15/7 + 12/7)/11 = 27/77 ≈ 35.1%, approximately 35%.

Multiple choice

____ litre mixture of alcohol and water contain alcohol and water in the ratio 2.66. On adding 2.7 litres of water, the ratio of alcohol to water becomes 2:3. Further on adding ____ litre alcohol; the original ratio of alcohol to water is obtained. Find the missing figures. शराब और पानी के ____ लीटर मिश्रण में 2.66 अनुपात में अल्कोहल और पानी है। 2.7 लीटर पानी मिलाने पर शराब और पानी का अनुपात 2:3 हो जाता है। आगे ____ लीटर शराब मिलाने पर; पानी में शराबल और पानी का मूल अनुपात प्राप्त होता है। लापता आंकड़े का पता लगाएं।

  1. 3.3, 6

  2. 2.2, 7.2

  3. 1.1, 3.6

  4. 3.3, 7.2

  5. 7.2, 3.3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let initial mixture be 8+3=11 parts with ratio 8:3. After adding 2.7L water, ratio becomes 2:3. Working backwards: if 2.7L water changes ratio from 8:3 to 2:3, then initial alcohol = (2/5)×total = x×11/8. Solving gives initial volume = 3.3L. To restore 8:3 from 2:3, add 7.2L alcohol. Verified: 3.3, 7.2 matches option D.

Multiple choice

In ____ liters mixture of solution of salt and water; 0.25 part is salt. _____ liter water is evaporated so that the part of the salt in the final solution of 54 liter becomes 0.35. Find the missing figures. नमक और पानी के _____ लीटर मिश्रण में 0.25 हिस्सा नमक है. _____ लीटर पानी वाष्पित करने पर 54 लीटर के अंतिम मिश्रण में नमक का हिस्सा 0.35 हो गया। लापता आंकड़े का पता लगाएं।

  1. 8.1, 5.4

  2. 81, 5.4

  3. 75.6, 21.6

  4. 81, 54

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

Let initial mixture be V liters with 0.25V salt. After evaporating x liters, volume = V-x = 54L, and salt becomes 0.35. Salt amount is constant: 0.25V = 0.35×54 = 18.9. So V = 18.9/0.25 = 75.6L. Water evaporated = 75.6 - 54 = 21.6L. Answer: 75.6, 21.6 matches option C.

Multiple choice

A man purchased 35 kg. of rice at the rate of Rs. 9.50 per kg and 30 kg. of wheat at the rate of Rs. 10.50 per kg. He mixed the two approximately at what price per kg should he sell the mixture to make 35% profit in the transaction? एक व्यक्ति 9.50 रू. प्रति किग्रा की दर से 35 किग्रा. चावल और 10.50 रू. प्रति किग्रा. की दर से 30 किग्रा. गेहूँ खरीदता है। वह दोनों को मिलाता है। वह मिश्रण को लगभग किस दर से बेचे कि पूरे सौदे में उसे 35% का लाभ हो?

  1. 12.75

  2. 13.25

  3. 13.5

  4. 13.75

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

Total cost = (35 × 9.50) + (30 × 10.50) = 332.50 + 315 = 647.50. For 35% profit, selling price = 647.50 × 1.35 = 874.125. Total weight = 65 kg. Selling price per kg = 874.125/65 ≈ 13.45. The closest option is 13.5, which matches the claimed answer.

Multiple choice

A container contains a mixture of water and milk in the ratio of 7 :5. When 9 litres of mixture is drawn out and the remaining part of the container is filled with 9 litres milk, the ratio of water to milk becomes 7 : 9. How many litres of water does the container have initially? (in litres) एक डिब्बे में 7 : 5 के अनुपात में पानी और दूध का मिश्रण है। जब 9 लीटर मिश्रण निकाला जाता है और डिब्बे के शेष भाग को 9 लीटर दूध से भर दिया जाता है, तो पानी और दूध का अनुपात 7 : 9 हो जाता है। डिब्बे में प्रारम्भ में कितने लीटर पानी है? (लीटर में)

  1. 16

  2. 24

  3. 21

  4. 18

  5. 25
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial water = 7x, milk = 5x (total = 12x). 9 litres drawn contains water = 9 × 7/12 = 5.25 L, milk = 9 × 5/12 = 3.75 L. After removal: water = 7x - 5.25, milk = 5x - 3.75. Adding 9 L milk: milk becomes 5x + 5.25. New ratio (7x - 5.25)/(5x + 5.25) = 7/9. Solving: 63x - 47.25 = 35x + 36.75, giving 28x = 84, so x = 3. Initial water = 7 × 3 = 21 L.

Multiple choice

In two vessels ratio of milk and water is 5:3 and 5:7 respectively. They are mixed together in 5:4 . Find the ratio of milk and water in the final mixture. दो पात्रों में दूध तथा पानी का अनुपात क्रमशः 5 : 3 तथा 5 : 7 है। इन्हें 5 : 4 के अनुपात में मिलाया जाता है। अन्तिम मिश्रण में दूध तथा पानी का अनुपात ज्ञात कीजिये।

  1. 77:63

  2. 101:91

  3. 107:93

  4. 115:101

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

Vessel 1 has ratio 5:3, so 5/8 milk and 3/8 water. Vessel 2 has ratio 5:7, so 5/12 milk and 7/12 water. Taking them in 5:4 ratio means 5 units from V1 and 4 units from V2. Milk from V1: 5 × (5/8) = 25/8. Water from V1: 5 × (3/8) = 15/8. Milk from V2: 4 × (5/12) = 20/12 = 5/3. Water from V2: 4 × (7/12) = 28/12 = 7/3. Total milk = 25/8 + 5/3 = (75 + 40)/24 = 115/24. Total water = 15/8 + 7/3 = (45 + 56)/24 = 101/24. Ratio = 115:101.