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

Milk and water are mixed in a vessel A as 5:3 and in vessel B as 1:5. For vessel C, if one takes equal quantities from A and B, find the ratio of milk to water in C?
  1. $17:31$
  2. $19:29$
  3. $19:31$
  4. $17:29$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In vessel A, ratio milk:water = 5:3, so milk = 5/8, water = 3/8. In vessel B, ratio milk:water = 1:5, so milk = 1/6, water = 5/6. Taking equal quantities from A and B: Total milk = 5/8 + 1/6 = (15+4)/24 = 19/24. Total water = 3/8 + 5/6 = (9+20)/24 = 29/24. Therefore ratio milk:water = 19:29. Option D (17:31) is incorrect, Option C (19:31) has wrong water value, Option A (17:31) is also incorrect.

Multiple choice

A mixture contains two liquid A and B in the ratio 4: 1. If 10 liters of the mixture is replaced with 10 litres of liquid B, the ratio becomes 2: 3. How many litres of liquid A was in the mixture?

  1. 10 litres

  2. 12 litres

  3. 16 litres

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

Let initial A = 4x, B = x. Total = 5x. After removing 10 litres (8A, 2B) and adding 10B: A = 4x-8, B = x-2+10 = x+8. New ratio (4x-8):(x+8) = 2:3. Cross-multiply: 3(4x-8) = 2(x+8). Solving: 12x-24 = 2x+16, so 10x = 40, x = 4. Initial A = 4x = 16 litres.

Multiple choice

The three vessels are X, Y and Z. The ratio of ingredients A and B in vessel X is 6: 5, the ratio of ingredients B and C in vessel Y is 7: 4 and the ratio of ingredients C and A in vessel Z is 3: 8 , the mixture of the three vessels is mixed in ratio of 2 : 5 : 8 and placed in a new vessel P, then what is the percentage of ingredient B in the new vessel ? (near to two decimal point )
  1. $37.27 %$
  2. $33.37 %$
  3. $23.23 %$
  4. $27.27 %$
  5. $None of the above$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Vessel X (ratio A:B = 6:5) gives B as 5/11 of mixture. Vessel Y (ratio B:C = 7:4) gives B as 7/11. Vessel Z (ratio C:A = 3:8) gives B as 0. Using mixing ratio 2:5:8, total B = 2(5/11) + 5(7/11) + 8(0) = 45/11. Total volume = 2+5+8 = 15. Percentage of B = (45/11)/15 x 100 = 27.27%.

Multiple choice

Find the correct relationship between given quantities, Find the quantity of milk initially in the solution of milk and water- Q1- When 17.5 liter water is added in the solution percentage of milk reduces from 25% to 20%. Q2- In mixture quantity of water is twice the quantity of milk but when 5.75 liter milk is added in solution, percentage of milk in solution becomes 40%.

  1. Q1 > Q2

  2. Q1 ≥ Q2

  3. Q1 < Q2

  4. Q1 ≤ Q2

  5. Q1 = Q2 or relationship cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For Q1: 0.25x/(x+17.5) = 0.20 gives x=70L total, so initial milk = 0.25×70 = 17.5L. For Q2: Initially water = 2×milk, so milk = y, water = 2y. After adding 5.75L milk: (y+5.75)/(3y+5.75) = 0.40 gives y=17.25L. Since 17.5 > 17.25, Q1 > Q2.

Multiple choice

In what ratio a mixture containing 20% milk should be mixed with another mixture containing 75% milk so that in the resultant mixture percentage of milk becomes 40%.

  1. 7 : 4

  2. 6 : 5

  3. 9 : 5

  4. 8 : 5

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

Use alligation method. Mean concentration (40%) is closer to 75% than to 20%, so more of the 75% mixture is needed. The ratio is (75 - 40) : (40 - 20) = 35 : 20 = 7 : 4. This means mix the 20% and 75% mixtures in the ratio 7:4. Option A is correct.

Multiple choice

If two equal vessels in which the ratio of milk and water mixture is 7: 4 and 6: 5, both the mixtures are kept in a new vessel, then find the percentage of milk in the new vessel?
  1. $59.09 %$
  2. $64.09 %$
  3. $53.09 %$
  4. $49.09 %$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Vessel 1: Milk:Water = 7:4 (total parts = 11). Vessel 2: Milk:Water = 6:5 (total parts = 11). Since vessels are equal, total mixture = 2 × 11 = 22 parts. Total milk = 7 + 6 = 13 parts. Percentage of milk = (13/22) × 100 = 59.09%.

Multiple choice

Jar A has ‘x’ ml mixture of milk and water, of which 40% is water. Jar B also has mixture of milk and water, of which 20% is water. The quantity of mixture in Jar B is twice that of Jar A. If the content of Jar B is emptied into Jar A completely and the resultant quantity of milk in Jar A is 198 ml, what is the value of ‘x’?

  1. 45

  2. 90

  3. 85

  4. 95

  5. 65
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Jar A has x ml with 40% water, so 60% milk = 0.6x ml milk. Jar B has 2x ml with 20% water, so 80% milk = 1.6x ml milk. When combined, total milk = 0.6x + 1.6x = 2.2x = 198 ml. Therefore, x = 198 ÷ 2.2 = 90 ml.

Multiple choice

A vessel contains a mixture of milk and water in the respective ratio of 10: 3. Twenty six litre of this mixture was taken out and replaced with 8 litre of water. If the resultant respective ratio of milk and water in the mixture was 5: 2, what was the initial quantity of mixture in the vessel? (In litre)

  1. 143

  2. 182

  3. 169

  4. 156

  5. 130
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let the initial quantity be 13x liters (since milk:water = 10:3). Initial milk = 10x, water = 3x. After removing 26 liters (which maintains 10:3 ratio): milk removed = 20L, water removed = 6L. Remaining milk = 10x-20, remaining water = 3x-6. After adding 8L water: new milk = 10x-20, new water = 3x-6+8 = 3x+2. The new ratio is 5:2, so (10x-20)/(3x+2) = 5/2. Cross-multiplying: 20x-40 = 15x+10. Solving: 5x = 50, x = 10. Initial quantity = 13×10 = 130L. Verifying: 10(10)-20 = 80L milk, 3(10)+2 = 32L water, ratio = 80:32 = 5:2 ✓

Multiple choice

In mixture I ratio of milk and water is 4:3 whereas in mixture II ratio of milk and water is 5:9. If equal quantities of these two are mixed to form new mixture III. Find the ratio of milk and water in mixture III.
  1. $11:14$
  2. $13:15$
  3. $7:6$
  4. $9:5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Mixture I: milk=4/7, water=3/7. Mixture II: milk=5/14, water=9/14. Equal quantities mixed: Average milk = (4/7 + 5/14)/2 = (8/14 + 5/14)/2 = 13/28. Average water = (3/7 + 9/14)/2 = (6/14 + 9/14)/2 = 15/28. Ratio milk:water = 13:15.

Multiple choice

Sunil mixes 80 kg sugar worth Rs 13.5 per kg with 120 kg sugar worth Rs 16 per kg. At what rate should he sell the mixture to gain 40%?

  1. 18

  2. 20

  3. 22

  4. 21
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total cost = 80 × 13.5 + 120 × 16 = 1080 + 1920 = Rs 3000. Total weight = 80 + 120 = 200 kg. Cost price per kg = 3000/200 = Rs 15. For 40% profit, selling price = 15 × 1.40 = Rs 21 per kg. Option D is correct. Options A, B, and C represent different percentage gains (approximately 20%, 33%, and 47% respectively) but not the required 40%.

Multiple choice

In two types of brass, the ratios of Copper to Zinc are 4:1, and 3:7 respectively. If the two types of brass are melted and mixed in the ratio 3:2 a new type of brass is obtained. Find the ratio of Copper to Zinc in this new type of brass.

  1. 2:1

  2. 3:2

  3. 2:3

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

Type 1 brass: Copper:Zinc = 4:1. For 3 units of Type 1, copper = 3 × 4 = 12 units, zinc = 3 × 1 = 3 units. Type 2 brass: Copper:Zinc = 3:7. For 2 units of Type 2, copper = 2 × 3 = 6 units, zinc = 2 × 7 = 14 units. When mixed: Total copper = 12 + 6 = 18 units. Total zinc = 3 + 14 = 17 units. Ratio Copper:Zinc = 18:17. Hmm, this doesn't match option B (3:2). Let me reconsider. Actually, the two types are mixed in ratio 3:2. This means we take 3 parts of Type 1 and 2 parts of Type 2, where each part is the same quantity. Type 1 (4:1) means 4 parts copper, 1 part zinc, total 5 parts. Type 2 (3:7) means 3 parts copper, 7 parts zinc, total 10 parts. When we take 3 parts of Type 1 and 2 parts of Type 2, we need to ensure we're comparing like quantities. Let's say 1 part = x units. Then 3 parts of Type 1 = 3x units total, containing (4/5) × 3x = 12x/5 copper and (1/5) × 3x = 3x/5 zinc. 2 parts of Type 2 = 2x units total, containing (3/10) × 2x = 6x/10 = 3x/5 copper and (7/10) × 2x = 14x/10 = 7x/5 zinc. Total copper = 12x/5 + 3x/5 = 15x/5 = 3x. Total zinc = 3x/5 + 7x/5 = 10x/5 = 2x. Ratio Copper:Zinc = 3x : 2x = 3:2. Option B is correct. Options A, C, and D represent different ratios.

Multiple choice

A 108 liters of milk and water in the ratio 5 : 7. What liters of the mixture should be taken out and replaced with pure milk so that the final mixture contains milk and water in equal proportions?

  1. 18

  2. 15

  3. 9

  4. 15.4
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial mixture: 108L with milk:water = 5:7, so milk = 45L, water = 63L. Let x liters be removed and replaced with milk. After removal, remaining milk = 45(1-x/108), water = 63(1-x/108). Adding x liters milk: new milk = 45(1-x/108)+x, water = 63(1-x/108). For equal quantities: 45(1-x/108)+x = 63(1-x/108). Solving: 45-45x/108+x = 63-63x/108, giving x = 18×63/108 = 15.4 liters.

Multiple choice

The ratio of copper and zinc in an alloy, German silver, was 21: 16, while the ratio of nickel and zinc was 7: 24. What was the ratio of copper: zinc: nickel in the alloy?
  1. $63 : 48 : 14$
  2. $21 : 6 : 7$
  3. $68 : 28 : 21$
  4. $17 : 21 : 4$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given Cu:Zn = 21:16 and Ni:Zn = 7:24. To find Cu:Zn:Ni, make Zn equal in both ratios. Cu:Zn = 63:48 (multiplying by 3), Ni:Zn = 14:48 (multiplying by 2). Thus Cu:Zn:Ni = 63:48:14. Option A matches this ratio. Option B has incorrect proportions. Option C and D don't maintain the given relationships.

Multiple choice

In a solution water is 45%. When 18 liters more water is added the new concentration of water becomes 60%. Find the initial quantity of water in the solution.

  1. 36 liter

  2. 27 liter

  3. 25.8 liter

  4. 21.6 liter
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the initial total solution be T liters. Water is 45% of T = 0.45T. After adding 18L water, new water = 0.45T + 18 and new total = T + 18. Given new water concentration is 60%: (0.45T + 18)/(T + 18) = 0.6. Solving: 0.45T + 18 = 0.6T + 10.8, so 7.2 = 0.15T, giving T = 48L. Initial water = 0.45 × 48 = 21.6L. Option A (36L) would mean initial total was 80L, which doesn't satisfy the 60% condition.

Multiple choice

In what ratio must two kinds of sugar at Rs 1.15 per kg and Rs 1.24 per kg be mixed so that by selling at Rs 1.50 per kg, 25% may be gained?

  1. 4: 5

  2. 5: 4

  3. 1: 1

  4. 2: 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Selling price = Rs. 1.50/kg with 25% profit means cost price = 1.50/1.25 = Rs. 1.20/kg. Using allegation method: cheaper sugar (1.15) and dearer sugar (1.24) must mix to give CP (1.20). Difference from mean: 1.24 - 1.20 = 0.04 and 1.20 - 1.15 = 0.05. Ratio = 0.04:0.05 = 4:5. Mix 4 parts of Rs. 1.24 sugar with 5 parts of Rs. 1.15 sugar.