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

The ratio milk and water in a container is in the ratio 1 : 3, if 5 litres of milk added to this mixture, then ratio of the mixture would be 1 : 2. Then what is the quantity of the new mixture? एक पात्र में दूध और पानी का अनुपात 1 : 3 है, यदि इस मिश्रण में 5 लीटर दूध मिला दिया जाय, तो मिश्रण का अनुपात 1 : 2 हो जाएगा | तदनुसार उस नए मिश्रण की कुल मात्रा कितनी है ?

  1. 32 litres/लीटर

  2. 40 litres/लीटर

  3. 42 litres/लीटर

  4. 45 litres/लीटर
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initially milk:water = 1:3, so milk = x, water = 3x, total = 4x. After adding 5 litres milk: milk = x + 5, water = 3x. New ratio: (x + 5)/3x = 1/2, so 2(x + 5) = 3x, giving 2x + 10 = 3x, so x = 10. Initial quantities: milk = 10 litres, water = 30 litres. After adding 5 litres milk: milk = 15, water = 30. Total = 15 + 30 = 45 litres. The ratio change lets us solve for the initial quantities.

Multiple choice

Five litres of water is added to a certain quantity of pure milk costing Rs. 3 per litre. If by selling the mixture at the same price as before, a profit of 20% is made, what is the amount of pure milk in the mixture? 3 रू. प्रति लीटर मूल्य वाले शुद्ध दूध की एक निश्चित मात्रा में 5 लीटर पानी मिलाया जाता है। यदि मिश्रण को पहले की ही तरह उसी मूल्य पर बेचा जाता है, 20% लाभ प्राप्त होता है। मिश्रण में शुद्ध दूध की मात्रा क्या है?

  1. 18 ltr./ली.

  2. 23 ltr./ली.

  3. 25 ltr./ली.

  4. 27 ltr./ली.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let milk = x liters at Rs. 3/liter, so cost = Rs. 3x. Mixture sells at Rs. 3/liter for revenue Rs. 3(x+5). At 20% profit: 3(x+5) = 1.20 × 3x, solving gives x = 25 liters.

Multiple choice

Milk and water are in the ratio of 3:2 in a mixture of 80 litres. How much water should be added so that the ratio of the milk and water becomes 2:3?

  1. 20 litres

  2. 25 litres

  3. 35 litres

  4. 40 litres
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial mixture: milk = (3/5) × 80 = 48 litres, water = (2/5) × 80 = 32 litres. After adding x litres of water, milk:water = 48:(32+x) = 2:3. Cross-multiplying: 3(48) = 2(32+x), giving 144 = 64 + 2x, so 2x = 80 and x = 40 litres. Verification: 48/(32+40) = 48/72 = 2/3 ✓

Multiple choice

In what ratio must 25% of alcohol be mixed with 50% of alcohol to get a mixture of 40% strength alcohol? 25% अल्कोहल को 50% अल्कोहल में किस अनुपात में मिलाया जाय ताकि प्राप्त मिश्रण में 40% अल्कोहल हो जाये?

  1. 1 : 2

  2. 2 : 1

  3. 2 : 3

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

Using alligation method: To find the ratio of 25% and 50% alcohol to get 40%, calculate the differences from the target. 50% - 40% = 10 parts of the 25% solution, and 40% - 25% = 15 parts of the 50% solution. The ratio is 10:15, which simplifies to 2:3. Therefore, 25% alcohol and 50% alcohol must be mixed in the ratio 2:3 to get a 40% mixture.

Multiple choice

Ramesh has three varieities of rice costing 18 Rs/kg,25 Rs/kg and 36 Rs/kg, In what ratio he should mix these three varieties so that on selling whole mixture at 23.10 Rs/kg he may get a profit of 10?

  1. 7:3:2

  2. 5:3:2

  3. 9:3:2

  4. 9:3:1

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

Selling price is 23.10 Rs/kg with 10% profit, so cost price of mixture = 23.10/1.1 = 21 Rs/kg. Using allegation method: first mix 18 and 36 to get average (18+36)/2 = 27. Then mix 27 with 25 in ratio to get 21. allegation: (27-21):(21-25) = 6:4 = 3:2. So 18:36 ratio is 1:1 (equal quantities). Taking 3 parts each of 18 and 36 gives average 27, then 9 parts of 27 with 6 parts of 25 in 3:2 ratio. Therefore final ratio = 9:3:2 for costs 18, 25, 36 respectively.

Multiple choice

A vessel have 60 litre mixture of milk and water containing milk and water in the ratio of 2 : 3 litre of mixture is replaced with pure milk so that the container will have milk and water in equal proportion. Find the value of x?

  1. 10

  2. 12

  3. 15

  4. 20

  5. 24
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial mixture: milk = (2/5) × 60 = 24 L, water = (3/5) × 60 = 36 L. After removing x litres: milk = 24(1 - x/60), water = 36(1 - x/60). Adding x litres of milk: new milk = 24(1 - x/60) + x = 24 + x - 24x/60 = 24 + 36x/60. New water = 36(1 - x/60) = 36 - 36x/60. Setting equal: 24 + 36x/60 = 36 - 36x/60 gives 72x/60 = 12, so x = 10.

Multiple choice

In what ratio milk and water be mixed so that on selling the mixture at the cost price there would be a profit of 10%? दूध और पानी को किस अनुपात में मिलाकर बेचा जाय कि प्राप्त मिश्रण को क्रय मूल्य में बेचने पर 10% का लाभ प्राप्त हो ?

  1. 1 : 5

  2. 1 : 10

  3. 5 : 1

  4. 10 : 1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let milk be m parts and water be w parts. Cost of milk per unit = 1, cost of water = 0. Total cost = m, total quantity = m + w. CP of mixture = m/(m+w). For 10% profit selling at CP, we need: SP = CP × 1.1 = cost price. This means the actual CP must be such that when sold at that price, we make 10% profit. If we sell at the milk's cost price, we need the mixture to cost 1/1.1 times the milk price. So m/(m+w) = 1/1.1 = 10/11. Cross-multiplying: 11m = 10m + 10w, so m = 10w. Therefore, ratio milk:water = 10:1.

Multiple choice

In what ratio a shopkeeper must add milk and water so that on selling mixture at 15% more than cost price of milk he may get a profit of 25?

  1. 2:23

  2. 23:2

  3. 5:1

  4. 1:5

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

Let milk = m, water = w. Cost price of mixture = m (assuming milk cost = 1 per unit). Selling price = 1.15m (15% above milk's cost). Required profit = 25%, so effective cost must be: 1.15m / 1.25 = 0.92m. This means only 92% is milk, so 8% is water. Ratio milk:water = 92:8 = 23:2. The mixture is diluted enough that selling at just 15% premium still gives 25% profit.

Multiple choice

What part of a mixture consisting of 80 litre mixture having 15\% water should be taken out and replaced with water so that the new percentage of water in the mixture may become 25\%?

  1. 1/5 part

  2. 2/9 part

  3. 2/15 part

  4. 2/17 part

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

Let x litres be removed. Initial water = 15% of 80 = 12 litres. After removing x litres and adding water: remaining water = 12 - 0.15x, new water = 12 - 0.15x + x = 12 + 0.85x. Total mixture remains 80 litres. We need (12 + 0.85x)/80 = 0.25. Solving: 12 + 0.85x = 20, so 0.85x = 8, x = 8/0.85 = 800/85 = 160/17. Fraction to remove = (160/17)/80 = 2/17.

Multiple choice

In two types of mixture, the ratio of milk and water are 2 : 11 and 5 : 21 respectively. In what proportion should the two types be mixed so that the ratio of milk to water in the mixture becomes 7 : 32 ? दो प्रकार के मिश्रणों में, दूध और पानी का अनुपात क्रमशः 2 : 11 और 5 : 21 है। किस अनुपात में दोनों प्रकार के मिश्रणों को मिलाया जाय कि मिश्रण में दूध का पानी से अनुपात 7 : 32 हो जाय?

  1. 2 : 1

  2. 2 : 3

  3. 1 : 5

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

Mix 1 has milk fraction 2/13, Mix 2 has 5/26. Target: 7/39. Using allegation: (5/26 - 7/39) : (7/39 - 2/13) = 1/78 : 1/39 = 1 : 2. Mix in ratio 1:2. This tests allegation method for mixture problems.

Multiple choice

In a mixture of milk and water, water is 30%. When 10 litre mixture is taken out and 15 litre water is added, water becomes 40%. Find initial quantity of mixture?

  1. 80 litre

  2. 75 litre

  3. 90 litre

  4. 100 litre

  5. 105 litre
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial mixture has 30% water. 10 litres removed means 3 litres water removed. Initial milk = 70% of M = 0.7M, water = 0.3M. After removal: milk = 0.7M - 7, water = 0.3M - 3. After adding 15 litres water: water = 0.3M + 12, total = M + 5. New percentage: (0.3M + 12)/(M + 5) = 40% = 0.4. Solving: 0.3M + 12 = 0.4M + 2, so 0.1M = 10, M = 100 litres.

Multiple choice

A solution of water and salt contains 8% salt. When 25 litre water is evaporated percentage of salt in solution becomes 12%. Find the initial quantity of mixture.

  1. 60 litre

  2. 75 litre

  3. 80 litre

  4. 100 litre

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

Let the initial quantity be x litres. Salt remains constant at 0.08x while total volume becomes (x-25) after evaporation. Setting 0.08x/(x-25) = 12% gives x = 75 litres. Option C (80) would result in 11.4% salt concentration, not 12%.

Multiple choice

In a mixture ratio of sprit and water is (5:3). When 15 litre mixture is taken out and replaced by 20 litre water, the quantity of sprit and water becomes equal. Find the quantity of sprit in the mixture initially?

  1. 45.8 litre

  2. 42.125 litre

  3. 59.375 litre

  4. 62.275 litre

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

Let initial spirit = 5x, water = 3x. Taking out 15 litres removes spirit=15*(5/8)=9.375 L, water=15*(3/8)=5.625 L. Remaining: spirit=5x-9.375, water=3x-5.625. After adding 20 L water: spirit=5x-9.375, water=3x-5.625+20=3x+14.375. These are equal, so 5x-9.375=3x+14.375, giving 2x=23.75, x=11.875. Initial spirit=5x=5*11.875=59.375 L. Option C is correct. Key distractor: A (45.8) likely comes from incorrectly assuming only water changes.

Multiple choice

Three containers A, B and C contains milk and water in ratio 4 : 1, 5 : 3 and 1 : 3. In what ratio they should mix together to make quantity of milk and water equal ?

  1. 4 : 3 : 5

  2. 15 : 17 : 25

  3. 11 : 9 : 16

  4. 5 : 2 : 7

  5. 7 : 15 : 11
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Container A: milk:water=4:1 (milk=4/5=80%), Container B: 5:3 (milk=5/8=62.5%), Container C: 1:3 (milk=1/4=25%). For equal milk and water in final mixture, overall milk percentage should be 50%. Using alligation: Container A (80%) and C (25%) can mix to give 50% in ratio 25:30 or 5:6. Container B (62.5%) needs to balance with lower percentage containers. Testing option D (5:2:7): Total milk = 5*4/5 + 2*5/8 + 7*1/4 = 4 + 1.25 + 1.75 = 7; Total water = 5*1/5 + 2*3/8 + 7*3/4 = 1 + 0.75 + 5.25 = 7. Equal, so D is correct.

Multiple choice

Ratio of volumes of two containers A and B is 3:5. Both containers are filled with milk and water and respective ratio is 5:4 and 8:7. If mixture of A and B is mixed in a third container C, find the ratio of milk and water in container C. दो पात्रों A तथा B के आयतन का अनुपात 3: 5 है। दोनों पात्र दूध और पानी से भरें है तथा अनुपात क्रमशः 5: 4 और 8: 7 है। यदि A और B को एक तीसरे पात्र C में मिलाया जाता है, तो पात्र C में दूध और पानी का अनुपात ज्ञात कीजिये ।

  1. 11:13

  2. 13:11

  3. 23:17

  4. 17:23
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let volumes be 3x and 5x. For A: milk:water = 5:4, so milk = 3x × 5/9 = 15x/9 = 5x/3, water = 3x × 4/9 = 12x/9 = 4x/3. For B: milk:water = 8:7, so milk = 5x × 8/15 = 40x/15 = 8x/3, water = 5x × 7/15 = 35x/15 = 7x/3. Total milk = 5x/3 + 8x/3 = 13x/3. Total water = 4x/3 + 7x/3 = 11x/3. Ratio = 13:11.