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

Manish bought 25 kg of rice at Rs.32 per kg and 15 kg of rice at Rs.36 per kg. What profit did he get when he mixed the two varieties together and sold it at Rs.40.20 per kg?

  1. 25%

  2. 40%

  3. 30%

  4. 20%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total cost = (25 × 32) + (15 × 36) = 800 + 540 = Rs.1340 for 40 kg rice. Cost price per kg = 1340/40 = Rs.33.50 per kg. Selling price = Rs.40.20 per kg. Profit per kg = 40.20 - 33.50 = Rs.6.70. Profit percent = (6.70/33.50) × 100 = 20%. Option D is correct. At 20% profit on Rs.33.50, the selling price is 33.50 × 1.20 = Rs.40.20, which matches.

Multiple choice

The ratio of milk and water in mixtures of four containers are 5 : 3, 2 : 1, 3 : 2 and 7 : 4 respectively. In which container is the quantity of milk, relative to water is minimum?

  1. First

  2. Second

  3. Third

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

Compare milk:water ratios as fractions: Container 1 (5:3 = 1.67), Container 2 (2:1 = 2.00), Container 3 (3:2 = 1.50), Container 4 (7:4 = 1.75). The minimum milk-to-water ratio is 1.5 in Container 3. Option B (Second) has ratio 2:1 = 2, which is higher. The question asks for minimum milk relative to water, meaning smallest ratio.

Multiple choice

A vessel contains some litres of pure milk. If 25 litres of water is added to the vessel, then the ratio between milk and water becomes 12:5. 17 litres of the mixture is drawn from the vessel and 10 litres of water is added to the mixture. Find the new ratio between milk and water.
  1. $8 : 5$
  2. $5 : 8$
  3. $6 : 5$
  4. $5 : 6$
  5. $Cannot be determined$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let milk = M. Adding 25L water gives ratio 12:5, so M:25 = 12:5, meaning M = 60L. Initial mixture: 60L milk + 25L water = 85L total. Ratio is 60:25 = 12:5 ✓. Drawing 17L mixture: milk removed = 17×(12/17) = 12L, water removed = 17×(5/17) = 5L. Remaining: milk = 60-12 = 48L, water = 25-5 = 20L. Adding 10L water: milk = 48L, water = 20+10 = 30L. New ratio = 48:30 = 8:5 ✓

Multiple choice

The ratio of the milk and water in two mixtures of 20 litre and 36 litre is 3 : 7 and 7 : 5 respectively. Both the mixtures are mixed together. Now the ratio of the milk and water in the new mixture is 20 लीटर और 36 लीटर के दो मिश्रणों में दूध और पानी का अनुपात क्रमशः 3 : 7 और 7 : 5 है |दोनों मिश्रणों को मिलाया गया है | अब नए मिश्रण में दूध और पानी का अनुपात है

  1. 25 : 29

  2. 9 : 10

  3. 27 : 29

  4. 27 : 31
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In first mixture (20L, ratio 3:7): milk = 3/10 × 20 = 6L, water = 7/10 × 20 = 14L. In second mixture (36L, ratio 7:5): milk = 7/12 × 36 = 21L, water = 5/12 × 36 = 15L. When mixed: total milk = 6 + 21 = 27L, total water = 14 + 15 = 29L. Ratio = 27:29. Option A (25:29) undercounts milk, option B (9:10) simplifies incorrectly, and option D (27:31) overcounts water.

Multiple choice

A shopkeeper mixes three varities of sugar costing Rs. 40 per kg, Rs. 48 per kg. and Rs. 60 per kg. and sells the mixture at a profit of 20% at Rs. 60 per kg. How many kgs of second variety will be in the mixture if 2 kgs of the third variety is there in the mixture ?

  1. 2

  2. 3.33

  3. 4

  4. 5

  5. Can't be determined
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Cost price of mixture = 60 / 1.20 = Rs. 50/kg (since sold at 20% profit). Using allegation: Let second variety be x kg. First variety (Rs. 40) and third variety (Rs. 60, 2 kg) mix to give Rs. 50. Ratio 40 : 60 = 10 : 10 = 1 : 1. So 2 kg of third variety needs 2 kg of first variety. Average of (40 and 60) is 50. Now allegation between average 50 (from 2+2=4kg) and second variety 48 to get 50: 50 is at 4:1 ratio from 48 and 50, so second variety = 4 × 1 = 4 kg. Wait, let me reconsider. (40×2 + 60×2)/(2+2) = 200/4 = 50. So 4 kg at Rs. 50. To maintain Rs. 50 when mixing with Rs. 48, we need ratio 48:50 = 2:2, meaning equal quantities. So 4 kg of Rs. 48 type.

Multiple choice

In an mixture the ratio of copper and zinc is 5 : 2. If 1.250 kg of zinc is mixed in 17.5 kg of alloy then the ratio of copper and zinc will be- किसी मिश्रण में तांबा और जस्ता का अनुपात 5 : 2 है। यदि 1.250 किग्रा. जस्ते को 17.5 किग्रा. मिश्रण में मिला दिया जाता है, तो तांबा और जस्ता का अनुपात होगा-

  1. 2 : 1

  2. 2 : 3

  3. 3 : 2

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

Original alloy 17.5 kg has copper:zinc = 5:2. Copper = (5/7)×17.5 = 12.5 kg, Zinc = (2/7)×17.5 = 5 kg. Adding 1.250 kg zinc: new zinc = 5 + 1.250 = 6.250 kg. New ratio copper:zinc = 12.5:6.25 = 2:1.

Multiple choice

15 liters of a mixture contains 20% alcohol and rest water. If 3 liters of water is added in it, then percentage of alcohol in the new mixture will be - 15 ली. मिश्रण में 20% एल्कोहल है और शेष पानी है। यदि इसमें 3 ली. पानी मिला दिया जाता है तो नये मिश्रण में एल्कोहल का प्रतिशत होगा –

  1. 20%

  2. 25%

  3. 33.33%

  4. 16.67%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Original mixture: 20% of 15L = 3L alcohol, 12L water. After adding 3L water, total = 18L, alcohol still = 3L. New percentage = (3/18)×100 = 16.67%. This is a dilution problem - alcohol amount stays constant while total volume increases.

Multiple choice

In a mixture of 25 litres, the ratio of acid to water is 4 : 1, Another 3 litre water is added to the mixture. The ratio of acid to water in the new mixture is
  1. $5: 2$
  2. $3: 5$
  3. $2: 5$
  4. $5: 3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In 25 litres, acid is 4×5 = 20 litres and water is 5 litres (since 4:1 ratio means 4 parts acid and 1 part water, total 5 parts). After adding 3 litres water, total water becomes 8 litres while acid remains 20 litres. The new ratio is 20:8 = 5:2 after dividing by 4. Therefore, option A is correct.

Multiple choice

A mixture contains milk and water in the ratio of 4 : 3. If 5 litre of water is added to the mixture the ratio becomes 4 : 5. The quality of milk in the given mixture is- एक मिश्रण में दूध और पानी का अनुपात 4 : 3 है। यदि 5 लीटर पानी इस मिश्रण में मिलाया जाता है, तो अनुपात 4 : 5 हो जाता है। दिये गये मिश्रण में दूध की मात्रा है-

  1. 12 litre/लीटर

  2. 10 litre/लीटर

  3. 14 litre/लीटर

  4. 16 litre/लीटर
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let milk = 4x, water = 3x. Adding 5 litres water gives 4x : (3x + 5) = 4 : 5. So 5(4x) = 4(3x + 5), giving 20x = 12x + 20, so 8x = 20, x = 2.5. Milk quantity = 4x = 10 litres.

Multiple choice

How much water should be added to 20 lit. pure milk that the mixture is sold at cost price and gets a profit of 25%. 20L शुद्ध दूध में कितना पानी मिलाया जाये कि मिश्रण को क्रय मूल्य पर बेचकर 25% का लाभ हो।

  1. 6L

  2. 4L

  3. 5L

  4. 10L
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Selling at cost price with 25% profit means SP = 1.25 × CP_milk. Let water added be x liters. Total quantity = 20+x, selling at CP of 20L milk. So 20×CP = (20+x)×0.8×CP. Solving: 20 = 16 + 0.8x, so 0.8x = 4, x = 5L. Options A, B, D don't satisfy this condition.

Multiple choice

Milk and water are mixed in a vessel A as 4:1 and in vessel B as 3:2. For vessel C, if one takes equal quantities from A and B, find the ratio of milk to water in C. दूध तथा पानी को बर्तन A में 4 : 1 के अनुपात में और बर्तन B में 3 : 2 के अनुपात में मिलाया गया | यदि बर्तन A और बर्तन B से सामान मात्रा में मिश्रण एक बर्तन C में लिया जाय तो उसमे दूध तथा पानी का अनुपात ज्ञात कीजिये|

  1. 3 : 7

  2. 10 : 7

  3. 7 : 10

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

Vessel A has ratio 4:1 (milk:water), so in any quantity from A, milk is 4/5 and water is 1/5. Vessel B has ratio 3:2, so milk is 3/5 and water is 2/5. Taking x liters from each: Milk from A = 4x/5, Milk from B = 3x/5, Total milk = 7x/5. Water from A = x/5, Water from B = 2x/5, Total water = 3x/5. The ratio in C is (7x/5):(3x/5) = 7:3. Options A, B, and C have incorrect milk-to-water ratios.

Multiple choice

Three containers of equal volume contains milk and water. The ratios of milk and water are 2 : 3, 3 : 4 and 4 : 5 respectively. Contents of these containers are poured in a large container. The ratio of milk and water in the large container is तीन समान धारिता के बर्तन जिनमें दूध और पानी है | दूध और पानी का अनुपात क्रमशः 2 : 3, 3 : 4 और 4 : 5 है | इन बर्तनों के द्रव को एक बड़े बर्तन में डाला जाता है | बड़े बर्तन में दूध और पानी का अनुपात ज्ञात कीजिये |

  1. 411 : 540

  2. 401 : 544

  3. 417 : 564

  4. 407 : 560
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Three containers have equal volume. Taking total volume as 3×(2+3) = 15, 3×(3+4) = 21, 3×(4+5) = 27. For LCM of denominators, scale: 2:3 becomes 2/5:3/5, 3:4 becomes 3/7:4/7, 4:5 becomes 4/9:5/9. Taking common denominator 315: milk = (2×63 + 3×45 + 4×35) = 126+135+140 = 401, water = (3×63 + 4×45 + 5×35) = 189+180+175 = 544. Ratio = 401:544.

Multiple choice

In one glass milk and water are mixed in the ratio 3 : 5 and in another glass they are mixed in the ratio 6 : 1 . In what ratio should the contents of the two glasses be mixed together, so that the new mixture contains milk and water in the ratio 1 : 1 ?
  1. $20 : 7$
  2. $8 : 3$
  3. $27 : 4$
  4. $25 : 9$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Glass 1 has milk:water = 3:5, so milk fraction = 3/8. Glass 2 has milk:water = 6:1, so milk fraction = 6/7. For final 1:1 ratio, milk fraction = 1/2. Using alligation: mix 3/8 and 6/7 to get 1/2. The ratio is (6/7 - 1/2):(1/2 - 3/8) = (5/14):(1/8) = 20:7. Option A is correct.

Multiple choice

A vessel contain some litters of pure milk, If 25 litter of water is added to the vessel, the ratio between milk and water becomes 12 : 5, if now 17 litters of mixture is drawn from the vessel and 10 litters of water is added to it, then find the new ratio between milk and water?

  1. 5 : 8

  2. 8 : 5

  3. 3 : 2

  4. 2 : 3

  5. 10 : 3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initially, milk:water = 12:5 after adding 25L water, so milk = 60L (12×5), water = 25L. Total = 85L. When 17L mixture is removed, milk removed = 17×(12/17) = 12L, water removed = 17×(5/17) = 5L. Remaining: milk = 48L, water = 20L. Adding 10L water gives final ratio 48:30 = 8:5.