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

A 30 litres mixture is made up of 2 components (C1 and C2) in the ratio 3 : 2. If some quantity of the mixture is taken out and 6 litres of C1 and 6 litres of C2 is added to the mixture, then the ratio of C1 and C2 becomes 6 : 5. What is the quantity of mixture which was taken out initially?

  1. 14 litres

  2. 20 litres

  3. 27 litres

  4. 32 litres

  5. 36 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial mixture: 18L C1, 12L C2. Let x be the amount taken out. Remaining: (18 - 0.6x) C1, (12 - 0.4x) C2. Adding 6L of each: (24 - 0.6x) / (18 - 0.4x) = 6/5. Solving for x: 120 - 3x = 108 - 2.4x, 12 = 0.6x, x = 20.

Multiple choice

The ratio of white balls and black balls in a container is 8 : 5. If 10 white balls are taken out from the container and 15 new black balls are added in the container, the ratio of white balls and black balls will be 3 : 4. How many white balls were there in the container initially?

  1. 35

  2. 37

  3. 40

  4. 42

  5. 45
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial ratio 8x:5x. (8x - 10) / (5x + 15) = 3/4. 32x - 40 = 15x + 45. 17x = 85, x = 5. White balls = 8 * 5 = 40.

Multiple choice

Two batches of drinks are prepared by using mixture of Vodka and Juice. In the first batch, the ratio of Vodka and Juice is 5 : 4 and in second batch, the ratio is 2 : 7. If 9 litres of drink from first batch and 27 litres of drink from second batch is taken and mixed together to make a new drink, then calculate the ratio of Vodka and juice in the new batch.

  1. 11 : 25

  2. 3 : 4

  3. 1 : 6

  4. 7 : 3

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

Batch 1: 9 litres, ratio 5:4. Vodka = 5, Juice = 4. Batch 2: 27 litres, ratio 2:7. Vodka = 27*(2/9) = 6, Juice = 27*(7/9) = 21. Total Vodka = 5 + 6 = 11. Total Juice = 4 + 21 = 25. Ratio = 11:25.

Multiple choice

A vessel X contains 119 litres of mixture of acetic acid and water in the ratio of 10 : 7. 34 litres of mixture is taken out from vessel X and poured into a vessel Y, in which the ratio of acetic acid and water is 8 : 5. The final quantity of acetic acid in vessel Y is 26 litres more than the final quantity of acetic acid in vessel X. Find the final quantity of water in the vessel Y.

  1. 39 litres

  2. 49 litres

  3. 29 litres

  4. 35 litres

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

A chemical production company dilutes a chemical by mixing it with water. The new mixture of 170 litres contains chemical and water in 27 : 7 proportion. Later, the company decides to further dilute the mixture to form a new mixture containing chemical and water in 3 : 1 proportion. How much water must they add in the previous mixture?

  1. 10 litres

  2. 7.5 litres

  3. 5 litres

  4. 12 litres

  5. 15 litres
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial mixture: 170 liters, 27:7 ratio. Chemical = (27/34)*170 = 135, Water = (7/34)*170 = 35. To get 3:1 ratio, 135 / (35 + x) = 3 / 1. Solving gives 135 = 105 + 3x, so 3x = 30, x = 10.

Multiple choice

McGrath earned a profit of Rs. 300 by selling 100 kg of a mixture of A and B types of rice at a total price of Rs. 1100. What was the proportion of A and B types of rice in the mixture, if the cost prices of A and B were Rs. 10 per kg and Rs. 5 per kg, respectively?

  1. 3 : 2

  2. 13 : 18

  3. 2 : 3

  4. 8 : 11
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total quantity = 100 kg, Total SP = 1100, Profit = 300, so Total CP = 800. Let A = x, B = 100-x. 10x + 5(100-x) = 800. 10x + 500 - 5x = 800. 5x = 300, x = 60. A = 60, B = 40. Ratio = 60:40 = 3:2.

Multiple choice

Two alloys A and B contain gold and copper in the ratios of 2 : 3 and 3 : 7 by mass, respectively. Equal masses of alloys A and B are melted to make an alloy C. The ratio of gold to copper in alloy C is _____.

  1. 5 : 10

  2. 7 : 13

  3. 6 : 11

  4. 9 : 13
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Alloy A has gold/copper ratio 2:3 (2/5 gold). Alloy B has 3:7 (3/10 gold). Equal masses mean we average the fractions: (2/5 + 3/10) / 2 = (7/10) / 2 = 7/20 gold. Copper is 1 - 7/20 = 13/20. The ratio is 7:13.

Multiple choice

A container contains a mixture of propene and methane in the ratio 5 : 1. Eighteen litres of mixture is taken out from the container and 6 litres of pure methane is added in the container. If the resultant ratio between propene and methane in the container is 3 : 1, what was the initial quantity (in litres) of the mixture in the container before replacement?

  1. 54

  2. 62

  3. 72

  4. 84

  5. 92
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial propene be 5x and methane be x. Total = 6x. Removing 18L removes 15L propene and 3L methane. Remaining: 5x - 15 propene, x - 3 methane. Adding 6L methane: 5x - 15 propene, x + 3 methane. Ratio (5x - 15) / (x + 3) = 3 / 1. 5x - 15 = 3x + 9, so 2x = 24, x = 12. Initial mixture = 6 * 12 = 72L.

Multiple choice

Tin and Cobalt are mixed in the respective ratio of 1 : 2 to form an alloy 1. Later, they are mixed in the ratio of 2 : 3 to form alloy 2. Then, these two alloys are mixed to form another alloy in which tin to cobalt ratio is 5 : 8. What is the ratio of alloy 1 to alloy 2 in the newly formed alloy?

  1. 3 : 10

  2. 3 : 7

  3. 10 : 3

  4. 7 : 3

  5. 4 : 7
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the alligation method: Alloy 1 has 1/3 tin, Alloy 2 has 2/5 tin, and the mixture has 5/13 tin. The differences are |2/5 - 5/13| = 1/65 and |1/3 - 5/13| = 2/39. The ratio is (1/65) / (2/39) = (1/65) * (39/2) = 39/130 = 3/10.

Multiple choice

A juice maker makes juice of orange in soda (according to the customers' needs). Today, he made 54 l of 24% orange juice and kept it ready in a 54 l delivery container to be shipped to the customer. Just before delivery, he found out that the customer had asked for 54 l of 42% orange juice. To make what the customer wants, the juice maker replaced a portion of 24% juice by 78% juice. How much (in l) of 24% juice is replaced?

  1. 20 litres

  2. 16 litres

  3. 18 litres

  4. 14 litres

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

Let x be the amount of 24% juice replaced by 78% juice. 54 * 0.24 - x * 0.24 + x * 0.78 = 54 * 0.42. 12.96 + 0.54x = 22.68. 0.54x = 9.72. x = 18.