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

Passage

Read the following information carefully to answer the questions asked- पूछे गए प्रश्नों का उत्तर देने के लिए निम्नलिखित जानकारी को ध्यान से पढ़ें- There are four containers A, B, C and D. Each contains mixture of milk, honey and water. Related information are given below. चार कंटेनर A, B, C और D हैं। प्रत्येक में दूध, शहद और पानी का मिश्रण है। संबंधित जानकारी नीचे दी गई है। (1) A contains 40 liter milk which is more than the quantity of milk in B and 25% more than the quantity of milk in D. (2) Ratio of milk, honey and water in C is 3:1:2 and that in A is 8:5:7. (3) Total mixture quantity in B and C is 20 and 50 liters more than that of A. (4) In B quantity of water is 250% of that of honey in same mixture. (5) In D total quantity of honey and water is 51 liter more than that of milk in same mixture and honey is 17 liter more than water. (1) A में 40 लीटर दूध है जो B में दूध की मात्रा से अधिक है और D में दूध की मात्रा से 25% अधिक है। (2) C में दूध, शहद और पानी का अनुपात 3:1:2 है और A में 8:5:7 है। (3) B और C में कुल मिश्रण की मात्रा A की तुलना में 20 और 50 लीटर अधिक है। (4) B में पानी की मात्रा समान मिश्रण में शहद की मात्रा का 250% है। (5) D में शहद और पानी की कुल मात्रा समान मिश्रण में दूध की तुलना में 51 लीटर अधिक है और शहद पानी से 17 लीटर अधिक है।

If same quantity of A and B are mixed together find the ratio of milk, honey and water in resultant mixture. यदि A और B की समान मात्रा को एक साथ मिलाया जाता है तो परिणामी मिश्रण में दूध, शहद और पानी का अनुपात ज्ञात कीजिये।

  1. 12:9:17

  2. 14:8:17

  3. 14:9:27

  4. 14:12:17

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

This question requires the composition ratios of mixtures A and B from the data interpretation set. Equal quantities of A and B means adding the corresponding components. Without the original ratios of milk:honey:water for A and B, the resultant ratio cannot be calculated.

Multiple choice

Passage

Read the following information carefully to answer the questions asked- पूछे गए प्रश्नों का उत्तर देने के लिए निम्नलिखित जानकारी को ध्यान से पढ़ें- There are four containers A, B, C and D. Each contains mixture of milk, honey and water. Related information are given below. चार कंटेनर A, B, C और D हैं। प्रत्येक में दूध, शहद और पानी का मिश्रण है। संबंधित जानकारी नीचे दी गई है। (1) A contains 40 liter milk which is more than the quantity of milk in B and 25% more than the quantity of milk in D. (2) Ratio of milk, honey and water in C is 3:1:2 and that in A is 8:5:7. (3) Total mixture quantity in B and C is 20 and 50 liters more than that of A. (4) In B quantity of water is 250% of that of honey in same mixture. (5) In D total quantity of honey and water is 51 liter more than that of milk in same mixture and honey is 17 liter more than water. (1) A में 40 लीटर दूध है जो B में दूध की मात्रा से अधिक है और D में दूध की मात्रा से 25% अधिक है। (2) C में दूध, शहद और पानी का अनुपात 3:1:2 है और A में 8:5:7 है। (3) B और C में कुल मिश्रण की मात्रा A की तुलना में 20 और 50 लीटर अधिक है। (4) B में पानी की मात्रा समान मिश्रण में शहद की मात्रा का 250% है। (5) D में शहद और पानी की कुल मात्रा समान मिश्रण में दूध की तुलना में 51 लीटर अधिक है और शहद पानी से 17 लीटर अधिक है।

What quantity of mixture from A should replace with honey so that new ratio of milk, honey and water in A becomes 8:10:7? A से मिश्रण की कितनी मात्रा शहद के साथ बदलना चाहिए ताकि A में दूध, शहद और पानी का नया अनुपात 8:10:7 हो जाए?

  1. 10

  2. 12

  3. 15

  4. 20

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

This replacement problem requires knowing the current ratio of milk:honey:water in mixture A from the data interpretation chart. The replacement quantity depends on the current composition, which is not provided in this isolated question.

Multiple choice

Passage

In the questions given below some data is not given and answer by filling in the appropriate data.

A vessel contain 144 liters of milk and water. The ratio of milk and water is 5:4. If --------- liters of mixture is taken out from the vessel and then ---------liters of water is added to it, so 46.875 % will be the percentage of milk in the final mixture. A. 71 B. 36 C. 15 D. 20 E. 45

  1. C, B

  2. B, C

  3. C, E

  4. B, D

  5. B, E
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial milk: 5/9 × 144 = 80L, water: 4/9 × 144 = 64L. Let x liters removed and y liters added. After removal: milk = 80 - (5/9)x, water = 64 - (4/9)x. After adding y liters water: milk = 80 - (5/9)x, total = 144 - x + y. Required: (80 - 5x/9)/(144 - x + y) = 46.875% = 15/32. Testing x=36, y=20: (80 - 20)/(144 - 36 + 20) = 60/128 = 15/32 ✓

Multiple choice

Passage

Directions: In the following item, quantity I and quantity II are given. Determine the relationship between the quantities and choose the appropriate option. (1) If Quantity I ≥ Quantity II (2) If Quantity I > Quantity II (3) If Quantity I < Quantity II (4) If Quantity I = Quantity II or the relationship cannot be established from the information given (5) If Quantity I ≤ Quantity II

A drum has 120 litres of a mixture containing milk and water in the ratio 5 : 1. Quantity I: The proportion of milk in the mixture after adding 30 litres of water. Quantity II: The proportion of milk in the mixture after 30 litres of mixture is replaced with water.

  1. (1)

  2. (2)

  3. (3)

  4. (4)

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

Initial: 100 milk, 20 water. Q1: Add 30 water -> 100 milk, 50 water. Proportion = 100/150 = 2/3. Q2: Replace 30 mixture (5:1 ratio, 25 milk, 5 water) with 30 water. Milk left = 100 - 25 = 75. Total = 120. Proportion = 75/120 = 5/8. 2/3 (0.66) > 5/8 (0.625).

Multiple choice

Passage

Directions: Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You are to use the given data and your knowledge of Mathematics to choose among the given options.

Quantity I: Wine costing \$40 per litre is mixed with wine costing \$50 per litre such that the mixture costs \$44 per litre. Calculate the percentage of wine costing \$40 in the mixture. Quantity II: Vodka costing \$54 per litre is mixed with vodka costing \$60 per litre so as to earn a profit of 15% after selling the mixture for \$64.4 per litre. Calculate the percentage of vodka costing \$54 in the mixture.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I = Quantity II or no relation can be established.

  5. Quantity I ≤ Quantity II
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: Using alligation, (50-44)/(44-40) = 6/4 = 3/2. Ratio of 40:50 is 3:2. Percentage of 40 = 3/(3+2) = 60%. Quantity II: Selling price = 64.4, profit = 15%. Cost price = 64.4 / 1.15 = 56. Using alligation, (60-56)/(56-54) = 4/2 = 2/1. Ratio of 54:60 is 2:1. Percentage of 54 = 2/(2+1) = 66.67%. 60% < 66.67%.

Multiple choice

Passage

Directions: Answer the question on the basis of the information given below. PQR Forgings manufactures a special alloy called Alloy-X using two metals − Metal-A and Metal-B. For manufacturing Alloy-X, 44% of Metal-A and 27% of Metal-B are required. The manufacturing of Alloy-X happens only in lots of 100 kg and manufacturing of any lot of Alloy-X can begin only if the quantities of metals available are sufficient to manufacture 100 kg of Alloy-X. Further, only when there is a shortfall in any metal, because of which it is not possible to manufacture the subsequent lot of Alloy-X, is that metal extracted from its ore. Given below is a table of PQR Forgings, regarding the number of lots of Alloy-X manufactured on each day and the type and quantity of metals extracted from its ore, if any. The entries in the table on any day were made in the chronological order. Day Quantity of Alloy-X Manufactured (In kg) Quantity of Metal-A Extracted from its Ore (In kg) Quantity of Metal-B Extracted from its Ore (In kg) Day-1 700 - - Day-2 800 - - Day-3 500 500 - Day-4 500 - 400 Day-5 700 600 - Day-6 700 - 300 Day-7 600 800 - Day-8 600 - 400 Day-9 700 - - Day-10 600 300 -

Which of the following could be the total quantity of Metal-A and Metal-B combined after exactly 38 lots were manufactured?

  1. 389 kg

  2. 393 kg

  3. 410 kg

  4. 406 kg
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Passage

Directions: Each of the bottles mentioned in this question contains 50 ml of liquid. The liquid in any bottle can be 100% pure content (P) or can have certain amount of impurity (I). Visually it is not possible to distinguish between P and I. There is a testing device which detects impurity, as long as the percentage of impurity in the content tested is 10% or more. For example, suppose bottle 1 contains only P, and bottle 2 contains 80% P and 20% I. If content from bottle 1 is tested, it will be found out that it contains only P. If content of bottle 2 is tested, the test will reveal that it contains some amount of I. If 10 ml of content from bottle 1is mixed with 20 ml content from bottle 2, the test will show that the mixture has impurity, and hence we can conclude that at least one of the two bottles has I. However, if 10 ml of content from bottle 1 is mixed with 5 ml of content from bottle 2. the test will not detect any impurity in the resultant mixture.

5 ml of content from bottle A is mixed with 5 ml of content from bottle B. The resultant mixture, when tested, detects the presence of I. If it is known that bottle A contains only P, what BEST can be concluded about the volume of I in bottle B?

  1. 10 ml

  2. 1 ml

  3. 10 ml or more

  4. Less than 1 ml
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The test detects impurity if the concentration is >= 10%. Mixing 5ml of P (0% impurity) and 5ml of B (x% impurity) results in 10ml with (5/10)*x = 0.5x% impurity. Since the test detects impurity, 0.5x >= 10, so x >= 20%. 20% of 50ml is 10ml.

Multiple choice

Passage

Directions: A dishonest juice seller mixed some water into pure fruit juice and sold it to four shopkeepers X, Y, Z, and W in the same order. After mixing, the ratio of juice to water became 4 : 1. The table below shows how the juice seller handled the transactions: Shopkeepers Quantity Sold (in Litres) Juice Added (in Litres) Water Added (in Litres) Mixture Left (in Litres) X 110 50 0 500 Y M 34 9 N Z 98 3r r P W 95 3r - 6 r T

If the quantity of juice-water mixture before selling to X was V liters, then find the value of V.

  1. 720

  2. 600

  3. 560

  4. 540

  5. 800
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Before selling to X, the seller had V litres and added 50 litres of juice. After selling 110 litres, 500 litres remained, so V + 50 - 110 = 500. Hence, V = 560 litres.

Multiple choice

Passage

Directions: A dishonest juice seller mixed some water into pure fruit juice and sold it to four shopkeepers X, Y, Z, and W in the same order. After mixing, the ratio of juice to water became 4 : 1. The table below shows how the juice seller handled the transactions: Shopkeepers Quantity Sold (in Litres) Juice Added (in Litres) Water Added (in Litres) Mixture Left (in Litres) X 110 50 0 500 Y M 34 9 N Z 98 3r r P W 95 3r - 6 r T

If the ratio of juice to water just before selling to Z was 40 : 9, then find the total quantity of mixture just before selling to Z.

  1. 383 liters

  2. 343 liters

  3. 337 liters

  4. 355 liters

  5. 320 liters
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Passage

Directions: A dishonest juice seller mixed some water into pure fruit juice and sold it to four shopkeepers X, Y, Z, and W in the same order. After mixing, the ratio of juice to water became 4 : 1. The table below shows how the juice seller handled the transactions: Shopkeepers Quantity Sold (in Litres) Juice Added (in Litres) Water Added (in Litres) Mixture Left (in Litres) X 110 50 0 500 Y M 34 9 N Z 98 3r r P W 95 3r - 6 r T

If the difference between the quantities of juice and water in the mixture before selling to W is 171 liters, then find the value of r (If the ratio of juice to water just before selling to Z was 40 : 9).

  1. 3

  2. 5

  3. 8

  4. 13

  5. 22
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Passage

Directions: A dishonest juice seller mixed some water into pure fruit juice and sold it to four shopkeepers X, Y, Z, and W in the same order. After mixing, the ratio of juice to water became 4 : 1. The table below shows how the juice seller handled the transactions: Shopkeepers Quantity Sold (in Litres) Juice Added (in Litres) Water Added (in Litres) Mixture Left (in Litres) X 110 50 0 500 Y M 34 9 N Z 98 3r r P W 95 3r - 6 r T

T is the the final quantity of juice water mixture left. If the ratio of juice to water just before selling to Z was 40 : 9 and the difference between juice and water in the mixture before selling to W is 171 liters. What is the value of T?

  1. 100 litres

  2. 150 litres

  3. 180 litres

  4. 208 litres

  5. 230 litres
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Passage

Directions: Study the following data carefully and answer the question that follows. A dishonest petrol dealer mixed some kerosene in petrol and sold it to three customers, P, Q, and R, in the same order. After mixing, the ratio of petrol to kerosene became 9:2, respectively. The table below shows how the exchange took place (The dealer sold 220 litres to person P and then he added 80 litres of petrol and 40 litres of kerosene. The same is given for Q and R). Customers Quantity sold (I) Petrol added (I) Kerosene added (I) Mixture left (I) P 220 80 40 1000 Q y 36 34 M R 260 25r 5r z

If the quantity of the mixture right before selling to P was 'X' litres, then find the value of X.

  1. 950

  2. 1000

  3. 1100

  4. 1250

  5. 1300
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The mixture ratio is 9:2 (petrol:kerosene). After selling 220L to P, 1000L remains. Before selling to P, the dealer added 80L petrol and 40L kerosene to the previous mixture. Let the initial mixture be M. M - 220 + 120 = 1000. M = 1100.

Multiple choice

Passage

Directions: Study the following data carefully and answer the question that follows. A dishonest petrol dealer mixed some kerosene in petrol and sold it to three customers, P, Q, and R, in the same order. After mixing, the ratio of petrol to kerosene became 9:2, respectively. The table below shows how the exchange took place (The dealer sold 220 litres to person P and then he added 80 litres of petrol and 40 litres of kerosene. The same is given for Q and R). Customers Quantity sold (I) Petrol added (I) Kerosene added (I) Mixture left (I) P 220 80 40 1000 Q y 36 34 M R 260 25r 5r z

If the ratio of petrol to kerosene with the dealer just before selling to R is 10:3, then find the quantity of mixture the dealer has just before selling it to R.

  1. 420 litres

  2. 570 litres

  3. 650 litres

  4. 850 litres

  5. 920 litres
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Passage

Directions: Study the following data carefully and answer the question that follows. A dishonest petrol dealer mixed some kerosene in petrol and sold it to three customers, P, Q, and R, in the same order. After mixing, the ratio of petrol to kerosene became 9:2, respectively. The table below shows how the exchange took place (The dealer sold 220 litres to person P and then he added 80 litres of petrol and 40 litres of kerosene. The same is given for Q and R). Customers Quantity sold (I) Petrol added (I) Kerosene added (I) Mixture left (I) P 220 80 40 1000 Q y 36 34 M R 260 25r 5r z

If the difference between petrol and kerosene in the final mixture after selling to 'R' is 250 litres, then find the value of 'r'. If the ratio of petrol to kerosene with the dealer just before selling to R is 10 : 3.

  1. 2

  2. 3

  3. 4

  4. 5

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

Passage

Directions: Study the information carefully and answer the question that follows. A right circular conical vessel was filled with milk and water in the ratio 3 : 7. If x ml of mixture was sold and replaced with x ml of pure milk, the ratio of milk to water in the final mixture becomes 51 : 49. The quantity of mixture sold is 70 ml less than the initial quantity of mixture in the vessel.

Find the quantity of water in the final mixture.

  1. 49 ml

  2. 50 ml

  3. 63 ml

  4. 65.200 ml

  5. 67.400 ml
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial ratio 3:7. After replacing x ml, the ratio becomes 51:49. The total volume remains constant. Let initial volume be V. The amount of water changes from 0.7V to 0.7(V-x) = 0.49(V). Thus 0.7V - 0.7x = 0.49V, so 0.21V = 0.7x, x = 0.3V. Also, x = V - 70. So 0.3V = V - 70, 0.7V = 70, V = 100. Final mixture volume is 100. Water = 0.49 * 100 = 49 ml.