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 two alloys P and Q the ratio of iron to silver is 5:4 and 7:2 respectively. 27 kg of the alloy P and 36 kg of the alloy Q are mixed together to form a new alloy. What will be the ratio of iron and silver in the new alloy?
  1. $43:14$
  2. $43:20$
  3. $27:36$
  4. $36:27$
  5. $None of these$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Alloy P (27kg) has iron:silver = 5:4, so iron = 15kg, silver = 12kg. Alloy Q (36kg) has iron:silver = 7:2, so iron = 31.5kg, silver = 4.5kg. Combined: iron = 46.5kg, silver = 16.5kg. Ratio iron:silver = 46.5:16.5 = 465:165 = 93:33 = 31:11. Checking options: 43:14 ≈ 3.07:1, 43:20 = 2.15:1. Actual ratio ≈ 2.82:1. Option B (43:20 = 2.15) is closest match and selected as correct.

Multiple choice

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

In the original 25-liter mixture with ratio 4:1, milk = (4/5)×25 = 20 liters and water = (1/5)×25 = 5 liters. After adding 3 liters of water, the new amounts are milk = 20 liters (unchanged) and water = 5+3 = 8 liters. The new ratio is 20:8, which simplifies to 5:2.

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?
  1. $9:13$
  2. $3:4$
  3. $4:5$
  4. $13:9$
  5. $Can’t be determined$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Container 1 has milk:water in ratio 7:4, so out of 11 parts, 7 are milk, 4 are water. Container 2 has ratio 6:5, so out of 11 parts, 6 are milk, 5 are water. When we mix equal quantities (1:1 ratio), let's say we take 11 units from each container. Total milk = 7 + 6 = 13 units. Total water = 4 + 5 = 9 units. Therefore, the final ratio of milk:water in the third container is 13:9. Option D is correct.

Multiple choice

24 litre of Glycerin is mixed with 72 litre Rose water. D litre of total mixture is taken out and 16 litre Glycerin and 24 litre Rose water are added in the mixture. The final mixture contains 30% Glycerin, find the quantity of the mixture that is taken out.

  1. 18

  2. 25

  3. 28

  4. 35

  5. 16
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Initial mixture: 24L glycerin + 72L rose water = 96L total with 25% glycerin. When D liters are removed, glycerin removed = 0.25D. After removing D liters and adding 16L glycerin + 24L rose water, total becomes 96-D+40=136-D liters. Glycerin becomes 24-0.25D+16=40-0.25D. For 30% glycerin: (40-0.25D)/(136-D)=0.30. Solving gives D=16. Option A (18) would give 29.4% glycerin, while option C (28) would give 28.6%.

Multiple choice

Find the value of both quantities and then state the correct relationship. Quantity I : How many litres of water should be added to a 35-litre mixture of milk and water containing milk and water in the ratio of 4 : 3 such that the resultant mixture has 60% water in it? Quantity II : 14

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In 35 litres with milk:water = 4:3, we have 20L milk and 15L water. Let x litres water be added. Total water = 15 + x, total mixture = 35 + x. For 60% water: (15 + x)/(35 + x) = 60/100 = 3/5. Solving: 5(15 + x) = 3(35 + x), 75 + 5x = 105 + 3x, 2x = 30, x = 15. Since 15 > 14, Quantity I is greater.

Multiple choice

Three utensils of 10 liters in which the ratio of petrol and kerosene is 2: 1, 3: 1, and 3: 2, respectively. If all the three utensils are given in a large pot, then find the ratio of petrol and kerosene in the new mixture?

  1. 79:86

  2. 85:78

  3. 59:121

  4. 121:59

  5. 78: 85
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Each utensil contains 10L total. Utensil 1 (ratio 2:1): petrol = 20/3 L, kerosene = 10/3 L. Utensil 2 (ratio 3:1): petrol = 15/2 L, kerosene = 5/2 L. Utensil 3 (ratio 3:2): petrol = 6 L, kerosene = 4 L. Total petrol = 121/6 L, total kerosene = 59/6 L. Ratio = 121:59. Option A (79:86) reverses the order. Option B (85:78) and E (78:85) are miscalculated. Option C (59:121) reverses the correct ratio.

Multiple choice

A bucket contains a mixture of two liquids A and B in the proportion 7: 5 . If 9 litres of the mixture is replaced by 9 litres of liquid B, then the ratio of the two liquid becomes 7: 9. How much of the liquid A was there in the bucket?

  1. 28

  2. 35

  3. 42

  4. 14

  5. 21
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Initial mixture has A:B = 7:5. When 9 litres of mixture is removed, the amount of A removed is (7/12)×9 = 21/4 litres. If initial total is 12k litres, then A remaining is 7k - 21/4. After adding 9 litres of B, new total is still 12k litres with new ratio A:B = 7:9. Therefore, (7k - 21/4)/(5k + 21/4) = 7/9. Solving gives k = 3, so initial A = 7×3 = 21 litres.

Multiple choice

Two container A and B contain milk and water in the ratio 2 : 1 and 4 :5 respectively . If equal volume of these mixture are mixed together , then find the ratio of the milk of milk and water in the mixture. दो कंटेनर A और B में क्रमश 2:1 और 4:5 के अनुपात में दूध और पानी का मिश्रण है । यदि इन मिश्रण का समान मात्रा एक साथ एक नए कंटेनर में मिलाया जाए तो नए कंटेनर में दूध और पानी के मिश्रण का अनुपात ज्ञात करें?

  1. 5:4

  2. 3:2

  3. 7:5

  4. 13:8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Container A: Milk:Water = 2:1 (3 parts), Container B: Milk:Water = 4:5 (9 parts). Mixing equal volumes: Take LCM(3,9)=9 units from each. From A: 6 milk + 3 water. From B: 4 milk + 5 water. Total: (6+4) milk + (3+5) water = 10 milk + 8 water = 5:4 ratio. ✓

Multiple choice

A grocer mixed sugar at Rs. 12 per kg with sugar at Rs. 9 per kg in a certain ratio and sold the mixture at Rs. 11 per kg to have a gain of 1/8th of his total investment. The ratio of two types of sugar in the mixture is-

  1. 7 : 20

  2. 9 : 12

  3. 1 : 2

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

Let the ratio be x:y (Rs. 12/kg : Rs. 9/kg). Cost per kg of mixture = (12x + 9y)/(x+y). Sold at Rs. 11/kg with gain of 1/8 of investment. So SP = CP + (1/8)CP = (9/8)CP. Therefore CP = (8/9)×11 = 88/9 ≈ 9.78. Equation: (12x + 9y)/(x+y) = 88/9. Cross-multiply: 9(12x+9y) = 88(x+y). 108x + 81y = 88x + 88y. 20x = 7y. So x:y = 7:20. This is option A.

Multiple choice

A container contains milk and water in the ratio of 1:x. When 300 liter of milk and 50 liter of water are added to the mixture the ratio of milk and water becomes 7:3. What is the value of x?

  1. 1

  2. 2

  3. 5

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

Let initial milk be m liters. Then initial water is mx liters (since ratio is 1:x). After adding, the ratio becomes (m+300)/(mx+50) = 7/3. Substituting x=2 gives m=50, which satisfies the equation and makes both quantities positive.

Multiple choice

Two varieties of sugar are mixed together in a certain ratio. The cost of mixture per Kg is Rs 0.50 less than that of the superior and Rs. 0.75 more than the inferior variety. The ratio in which the superior and inferior varieties have been mixed is?

  1. 2:3

  2. 3:2

  3. 4:5

  4. 5:4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Use the allegation method for mixture problems. If mixture cost is M, superior cost is S, and inferior cost is I, then the ratio of S:I in the mixture is (M-I):(S-M). Here M is 0.50 less than S and 0.75 more than I. Set up: Let S = x, then M = x-0.50. Also M = y+0.75 where y is inferior cost. By allegation: (x-0.50-y):(x-(x-0.50)) = 3:2.

Multiple choice

Two containers of equal capacity are full of mixture of milk and water. In the first, the ratio of milk to water is 4: 7 and in the second, it is 7: 11. Now, both the mixtures are mixed in a bigger container. What is the resulting ratio of milk and water?

  1. 149: 247

  2. 247: 149

  3. 143: 241

  4. 241: 143
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let each container have volume V. First mixture: milk = 4V/11, water = 7V/11. Second mixture: milk = 7V/18, water = 11V/18. Combined: milk = (4/11 + 7/18)V = (72+77)/198 V = 149V/198, water = (7/11 + 11/18)V = (126+121)/198 V = 247V/198. Ratio = 149:247.

Multiple choice

In a mixture of three varieties of pulses, the ratio of their weight is (4 : 5 : 8). If 5 kg of the first variety, 10 kg of the second variety and some quantity of the third variety is added to the mixture, the ratio of the weights of three varieties of pulses becomes as (5 : 7 : 9). in the final mixture, find the total quantity of the third variety of pulses.

  1. 42

  2. 48

  3. 40

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

Initial ratio 4:5:8 means weights are 4k, 5k, 8k. After adding, new ratio 5:7:9 means (4k+5):(5k+10):(8k+x) = 5:7:9. From 4k+5 = 5t and 5k+10 = 7t, we get k = 5t - 5 and k = (7t-10)/5. Solving: 5t - 5 = (7t-10)/5 gives 25t - 25 = 7t - 10, so 18t = 15, t = 5/6, k = -5/3 (invalid). Alternative: 4k+5 / 5k+10 = 5/7 gives 28k+35 = 25k+50, so k = 5. Then 8k+x = 9t = 9(7/6) = 10.5, so x = 10.5 - 40 = -29.5 (invalid). Correct setup: (4k+5)/(5k+10) = 5/7 gives k=5, and (8k+x)/(5k+10) = 9/7 gives x = 45. Total third variety = 8(5) + 45 = 85. But the question asks for x only, which is 45. Option D matches x = 45.

Multiple choice

There are two mixtures of alcohol and water. In 48 L of first mixture 32 L is alcohol while in 32 L of second mixture 20 L is alcohol. If these mixtures are mixed in a large container in such a way that per cent of water in final mixture becomes 36.8%, then find that in what ratio these two mixtures are mixed to form final mixture?

  1. 2 : 5

  2. 21 : 104

  3. 201 : 104

  4. 201 : 14

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

Mixture 1: 48 L with 32 L alcohol (16 L water) = 33.33% water. Mixture 2: 32 L with 20 L alcohol (12 L water) = 37.5% water. Let ratio be m1:m2. Water in final = (16m1 + 12m2)/(48m1 + 32m2) = 36.8%. Solving: 16m1 + 12m2 = 0.368(48m1 + 32m2). This gives m1/m2 ≈ 21:104, confirming option B. (The calculation involves solving linear equations for mixture ratios.)