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

Directions: Read the information given below carefully and answer the question that follows. In a 70-litre mixture of diesel and kerosene, the ratio of diesel to kerosene is 9 : 5. ______ litres of kerosene and ______ litres of diesel must be added to make the ratio of diesel to kerosene as 11 : 10. Which of the following values can be put into the above blanks, respectively? (i) 25, 10 (ii) 25, 42 (iii) 35, 21 (iv) 35, 25 (v) 45, 32

  1. Only (i), (iii) and (v)

  2. Only (i), (iii) and (iv)

  3. Only (i), (ii) and (v)

  4. Only (ii), (iii) and (v)

  5. Only (ii), (iii) and (iv)
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

A trader purchases 70 kg of tea at Rs. 15 per kg and 30 kg of tea at Rs. 18.50 per kg. If the packing charges are 2%, then at what price he must sell the mixture of two to gain 15%?

  1. Rs.18.83 per kg

  2. Rs.18 per kg

  3. Rs.18.50 per kg

  4. Rs.17.80 per kg
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total cost = (70 * 15) + (30 * 18.5) = 1050 + 555 = 1605. Packing charges 2% = 0.02 * 1605 = 32.1. Total cost = 1637.1. To gain 15%, sell at 1637.1 * 1.15 = 1882.665. Price per kg = 1882.665 / 100 = 18.82665, approx 18.83.

Multiple choice

We have two solutions of milk namely A and B. Solution A contains milk and water in the ratio of 2 : 3 and solution B contains the same in the ratio 5 : 1. In what ratio should the solutions A and B be mixed, such that new solution contains milk and water in the ratio 2 : 1?

  1. 2 : 3

  2. 1 : 3

  3. 1 : 8

  4. 5 : 8

  5. 3 : 8
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Solution A: 2/5 milk. Solution B: 5/6 milk. Target: 2/3 milk. Alligation: (5/6 - 2/3) : (2/3 - 2/5) = (1/6) : (4/15) = 5/30 : 8/30 = 5 : 8.

Multiple choice

A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9 of the marbles are removed, how many of the marbles left in the jar are red? (1) Of the marbles removed, the ratio of the number of red ones to the number of blue ones is 2 : 1. (2) Of the first 6 marbles removed, 4 are red.

  1. Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement (1) gives the ratio of removed marbles (2 red : 1 blue). Since 9 were removed, 6 were red and 3 were blue. Starting with 20 red, 20 - 6 = 14 red remain. Statement (2) only gives info on the first 6, not all 9, so it is insufficient.

Multiple choice

Two vessels of equal capacity contain water and alcohol. The first vessel, containing alcohol, is filled up to its maximum capacity, and the second vessel, containing water, is two-thirds empty. The content of the first vessel is poured into the second vessel to fill it to capacity and then the content of the second vessel is poured into the first vessel until it is full, and then again, the content of the first vessel is poured into the second vessel to fully fill it up. If we repeat the operation fourth time such that the first container is half-filled by pouring the content of the second container into it, then what will be the ratio of alcohol to water in the first container?

  1. 60 : 19

  2. 62 : 19

  3. 19 : 62

  4. 19 : 60

  5. 17 : 19
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is a complex vessel transfer problem. Following the steps carefully: Vessel 1 (V1) starts full of alcohol, Vessel 2 (V2) is 1/3 full of water. After the sequence of pours described, the ratio of alcohol to water in the first container is 62:19.

Multiple choice

A factory needs to obtain the right chemical solution which is a mix of sodium nitrate and molten caustic soda to give black finish to steel parts. In a trial process, 'c ' litres of the pure chemical solution was drawn from a furnace tank containing 729 litres of the pure chemical solution and replaced with water. The resulting mixture was thoroughly mixed to obtain a homogeneous aqueous solution and then again 'c' litres of this resulting solution was withdrawn and replaced with water. The resulting mixture was again thoroughly mixed to obtain a homogeneous aqueous solution. This procedure was repeated 6 times till the tank contained 64 litres of the pure chemical solution. Find the value of 'c'.

  1. 81

  2. 162

  3. 243

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

Final amount = Initial * (1 - c/729)^n. 64 = 729 * (1 - c/729)^6. (64/729) = (1 - c/729)^6. (2/3)^6 = (1 - c/729)^6. 2/3 = 1 - c/729. c/729 = 1/3. c = 243.

Multiple choice

A mixture of two miscible volatile ideal liquids P and Q (obeying Raoult's law) is kept in a vessel (molar ratio of P and Q in the mixture is m). At a suitable temperature T, the vapour above the liquid is condensed in another vessel. The liquid obtained on condensation is allowed to evaporate and establish equilibrium with its vapour. The vapour is then condensed in another vessel. The process of such evaporation and condensation is repeated for n times. If the ratio of the vapour pressure of pure P to that of pure Q is p, the molar ratio of P and Q in the condensed liquid obtained after nth cycle (for finite n > 1) is

  1. pnm

  2. pmn

  3. pn/2mn/2

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

In each distillation cycle, the ratio of the more volatile component increases by a factor of p. After n cycles, the enrichment factor is p^n. Therefore, the new ratio is p^n * m.

Multiple choice

Directions: In this problem, a question is given followed by three statements numbered (I), (II) and (III). Read the statements carefully and determine which of them is/are sufficient/necessary to answer the question. In a solution of milk and water, what is the quantity of milk? I. Ratio of milk to water in the solution is 5 : 3. II. If we replace 40 L of solution with water, ratio of milk to water will become 5 : 11. III. Adding 10 L of milk and 10 L of water to the solution makes the ratio of milk to water 3 : 2.

  1. Only statements I and II

  2. Only statements II and III

  3. Any two of the statements

  4. All three statements

  5. Only statement I and either statement II or statement III
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

I gives the ratio. II allows setting up an equation with the 40L replacement to find the total volume. III allows setting up an equation with the additions to find the total volume. Any two statements are sufficient to solve for the specific quantity of milk.

Multiple choice

Directions: The following problem consists of a question and two statements giving certain data. You have to decide whether the data given in the statements is sufficient for answering the question and then choose the correct option. A thoroughly blended biscuit mix includes only flour and baking powder. What is the ratio of the number of grams of baking powder to the number of grams of flour in the mix? (A) Exactly 9.9 grams of flour is contained in 10 grams of the mix. (B) Exactly 0.3 gram of baking powder is contained in 30 grams of the mix.

  1. Statement (A) alone is sufficient, but statement (B) alone is not.

  2. Statement (B) alone is sufficient but statement (A) alone is not.

  3. Both (A) and (B) together are sufficient, but none of them alone is sufficient.

  4. Both (A) and (B) independently are sufficient.

  5. Both (A) and (B) together are not sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement (A) provides the ratio of flour to the total mix, which allows calculating the ratio of baking powder to flour. Statement (B) provides the ratio of baking powder to the total mix, which also allows calculating the ratio of baking powder to flour. Since both statements independently allow for the determination of the ratio, both are sufficient.

Multiple choice

Directions: In the following problem, a question is followed by two statements (A) and (B). Read the statements carefully and determine which of the given statements is/are sufficient/necessary to answer the question. In a mixture, the ratio of milk to water is 2 : 1 by volume. If the ratio of milk to water is to be 1 : 2 by volume, then what is the volume of water to be further added? (A) Volume of initial mixture is 60 litres. (B) Volume of water in initial mixture is 20 litres.

  1. Statement (A) alone is sufficient but statement (B) alone is not.

  2. Statement (B) alone is sufficient but statement (A) alone is not.

  3. Both (A) and (B) together are sufficient but neither of them alone is sufficient.

  4. Both statements are sufficient independently.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Both statements provide enough information to determine the initial quantities and the change required to reach the target ratio. Statement A gives the total volume, and Statement B gives the specific volume of water.

Multiple choice

Directions: Compare Quantity I and Quantity II, using additional information centred above the two quantities if such information is given, and choose the correct option. A 500 ml solution contains only alcohol and water in certain ratio. If 100 ml of water is added to the solution, then the ratio of water to alcohol in the solution becomes 2 : 1. If then 'y' ml of alcohol is added to the solution, the ratio of water to alcohol becomes 2 : 3. Quantity I: Value of 'y' Quantity II: 300

  1. Quantity I ≥ Quantity II

  2. Quantity I > Quantity II

  3. Quantity I ≤ Quantity II

  4. Quantity I < Quantity II

  5. Quantity I = Quantity II or no relation
Reveal answer Fill a bubble to check yourself
B Correct answer