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Test Level 2: Mixtures and Alligations - 2 - CAT MCQ


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15 Questions MCQ Test - Test Level 2: Mixtures and Alligations - 2

Test Level 2: Mixtures and Alligations - 2 for CAT 2024 is part of CAT preparation. The Test Level 2: Mixtures and Alligations - 2 questions and answers have been prepared according to the CAT exam syllabus.The Test Level 2: Mixtures and Alligations - 2 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test Level 2: Mixtures and Alligations - 2 below.
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Test Level 2: Mixtures and Alligations - 2 - Question 1

A bus driver is driving a bus at a speed of 40 km per hour. After travelling at this speed for some time, he increases its speed to 55 km per hour. If he travels a total distance of 285 km and the total time taken for the journey is 6 hours, then how much distance does he travel at the speed of 55 km per hour?

Detailed Solution for Test Level 2: Mixtures and Alligations - 2 - Question 1

Total distance travelled = 285 km
Total time taken = 6 hours
Average speed of journey = 285/6 km/h
By alligation method,

Therefore, the ratio of time spent travelling at 40 km/h to that travelling at 55 km/h =
Total time of journey = 6 hours
Therefore,
Time of travel at 55 km/h = 3 hours
Therefore, distance travelled at this speed = 55 × 3 = 165 km
This is our required solution.

Test Level 2: Mixtures and Alligations - 2 - Question 2

Three pots have the same volume. The ratio of milk and water in the first, second and third pots is 3 : 2, 7 : 3 and 11 : 4, respectively. What is the ratio of milk and water in the new mixture if liquids of the three pots are mixed?  

Detailed Solution for Test Level 2: Mixtures and Alligations - 2 - Question 2

Required ratio = 61 : 29

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Test Level 2: Mixtures and Alligations - 2 - Question 3

Gold is 19 times and copper is 9 times as heavy as water. In what ratio should these metals be mixed so that the mixture is 15 times as heavy as water?  

Detailed Solution for Test Level 2: Mixtures and Alligations - 2 - Question 3

Applying the rule of alligation,

Gold : Copper = 6 : 4 = 3 : 2

Test Level 2: Mixtures and Alligations - 2 - Question 4

A certain alloy contains 5 parts of A and 3 parts of B by weight. Another alloy contains 6 parts of A and 7 parts of B by weight. How much amount of A (in lbs) in its pure state must be melted along with 20 lbs of the first alloy and 65 lbs of the second so as to produce a new alloy containing 40% of B by weight?  

Detailed Solution for Test Level 2: Mixtures and Alligations - 2 - Question 4

20 lbs of the first alloy contains 20 × 5/8 of A (in lbs) and 20 × 3/8 of B (in lbs).
65 lbs of the second alloy contains 65 × 6/13 of A (in lbs) and 65 × 7/13 of B (in lbs).
Suppose X lbs of pure A is required.
⇒ (X + 65 + 20) × 
⇒ X = 21.25 lbs

Test Level 2: Mixtures and Alligations - 2 - Question 5

Kalicharan gets some coins made of an alloy of gold and silver. The alloy with a weight of 100 gm contains 20% of gold. What weight of another gold-silver alloy containing 60% of silver must be alloyed with the first piece of alloy in order to obtain a new alloy with 32% of gold?  

Detailed Solution for Test Level 2: Mixtures and Alligations - 2 - Question 5

Gold in the first alloy = 20%
Gold in the second alloy = 40%
By alligation:

Ratio of the two alloys = 2 : 3
Quantity of the second alloy = 100 × 3/2 = 150 gm

Test Level 2: Mixtures and Alligations - 2 - Question 6

A shopkeeper had 10 kg of rice, bought at the rate of Rs. 40 per kg and bought another 30 kg of rice at the rate of 20 per kg and mixed the two. At what price per kg should he sell the mixture to get 15% profit on the cost price?  

Detailed Solution for Test Level 2: Mixtures and Alligations - 2 - Question 6

Cost price of the mixture = (10 × 40 + 30 × 20) = 1000
Selling price of the mixture = Cost price + (Cost price × 15%)
Selling price of the mixture = 1000 + 
Per kg selling price = = = 28.75

Test Level 2: Mixtures and Alligations - 2 - Question 7

Two equal containers are filled with a mixture of water and alcohol. One of them contains three times as much alcohol as the other. The mixtures in the two containers are then mixed and it is found that the ratio of water to alcohol is 3 : 2. Find the ratio of water to alcohol in each of the original containers.

Detailed Solution for Test Level 2: Mixtures and Alligations - 2 - Question 7

Let, the volume of each container = V
Now according to the question:
In container 1 W : A = V - 3x : 3x
In container 2 W : A = V - x : x
Now

V - 2x = 3x
V = 5x
So, In container 1 W : A = 2x : 3x = 2 : 3
In container 2 W : A = 4x : x = 4 : 1

Test Level 2: Mixtures and Alligations - 2 - Question 8

A merchant buys a brand of tea at Rs. 80 per kg and mixes it with another brand bought at Rs. 140 per kg. He makes a profit of 25% on selling the mixture at Rs. 125 per kg. What is the ratio in which the brands are mixed?  

Detailed Solution for Test Level 2: Mixtures and Alligations - 2 - Question 8

Selling price of the mixture = Rs. 125
Profit = 25%


Now, apply the rule of alligation:

Test Level 2: Mixtures and Alligations - 2 - Question 9

A vessel contains 40 litres of milk. A milkman delivers 10 litres to the first house and adds an equal quantity of water. He does the same with the second and the third houses. What is the ratio of milk to water when he has finished delivering at the third house?

Detailed Solution for Test Level 2: Mixtures and Alligations - 2 - Question 9

Total amount of milk = 40 litres
Amount of milk replaced by water = 10 litres
Now, ratio of milk to the total mixture = 
Water content in the mixture = 64 - 27 = 37
Hence, ratio of milk to water = 27 : 37

Test Level 2: Mixtures and Alligations - 2 - Question 10

Cask I contains wine and water in the respective ratio 6 : 7 and cask II contains wine and water in the respective ratio 9 : 4. In what ratio must the contents of the two casks be mixed to get a mixture of wine and water in the respective ratio 8 : 5?

Detailed Solution for Test Level 2: Mixtures and Alligations - 2 - Question 10


Test Level 2: Mixtures and Alligations - 2 - Question 11

A container is full of sugar syrup. 4 gallons of syrup is drawn out of the container and replaced with water. From this water-syrup mixture, 4 gallons of mixture is again withdrawn and replaced with water. The ratio of the sugar syrup to water in the container was then found to be 36 : 13. How many gallons does the container hold?

Detailed Solution for Test Level 2: Mixtures and Alligations - 2 - Question 11

Sugar : Water = 36 : 13
Sugar syrup in the container = of the total volume of the container.
After repeating the process twice, we have

Test Level 2: Mixtures and Alligations - 2 - Question 12

We have three solutions of milk A, B and C. Solutions A, B and C contain milk and water in the ratios of 1 : 3, 2 : 3 and 3 : 2, respectively. If we mix them in the ratio 1 : 2 : 3, respectively, then what is the ratio of milk and water in the new solution?

Detailed Solution for Test Level 2: Mixtures and Alligations - 2 - Question 12

Suppose we mix 1 L, 2 L and 3 L of A, B and C, respectively.
So, total milk in the solution would be = 1/4 + 4/5 + 9/5 = (5 + 16 + 36)/20 = 57/20
Total water in the solution would be= 3/4 + 6/5 + 6/5 = (15 + 24 + 24)/20 = 63/20
So, milk and water ratio in the new solution would be= 57 : 63 = 19 : 21

Test Level 2: Mixtures and Alligations - 2 - Question 13

Two metals X and Y are to be used for making two different alloys. If the ratio by weight of X : Y in the first alloy is 6 : 5 and that in the second is 7 : 13, then how many kilograms of X metal must be melted along with 11 kg of the first alloy and 20 kg of the second, so as to produce a new alloy containing 40% of metal Y?

Detailed Solution for Test Level 2: Mixtures and Alligations - 2 - Question 13

Let x kg of metal X be added.
Weight of metal X in the first alloy = 6/11 × 11 kg = 6 kg
Weight of metal X in the second alloy = 7/20 × 20 kg = 7 kg
Total weight of new alloy = (11 + 20 + x) kg
Total weight of metal X in the new alloy = (6 + 7 + x) kg.

130 + 10x = 186 + 6x
4x = 56
x = 14 kg

Test Level 2: Mixtures and Alligations - 2 - Question 14

A solution contains a mixture of liquid A and B in the ratio of 3 : 2. When 10 litre of solution is taken out and replaced by 10 litre of liquid B, the ratio of liquids A and B in the new solution is 1 : 2. What was the volume of the initial solution?

Detailed Solution for Test Level 2: Mixtures and Alligations - 2 - Question 14

Let the volume of initial solution be x litres.
So, the amounts of liquids A and B are 3x/5 and 2x/5, respectively.
When 10 litre of solution is taken out, the remaining liquid A in the solution would be

Quantity of liquid B in the new solution would be

So, the ratio of liquids A and B in the new solution would be

2(3x - 30) = 2x + 30
6x - 2x = 30 + 60
4x = 90
x = 22.5 litres

Test Level 2: Mixtures and Alligations - 2 - Question 15

Two containers contain a mixture of milk and water. In one container, the ratio of milk to water is 4 : 1 and the ratio of milk to water in the other container is 1 : 3. 10 litres of mixture from the first container and 16 litres of mixture from the second container is mixed together in a third container, already containing some amount of pure milk. In the new mixture, it was found that the ratio of milk to water was 3 : 2. Find the volume of the new mixture.

Detailed Solution for Test Level 2: Mixtures and Alligations - 2 - Question 15

10 litres of mixture from the 1st container is taken.
Thus, amount of milk in 1st mixture = 8 litres
16 litres of mixture from the 2nd container is taken.
Thus, amount of milk in 2nd mixture = 4 litres
Total milk after mixing two mixtures = 12 litres
Total amount of mixture = 26 litres
Fraction of milk in new mixture = 
Fraction of milk in 3rd container containing some pure milk = 1
Fraction of milk in the final mixture = 
By Alligation method:

Therefore, the ratio of two mixtures to pure milk will be
= 26 : 9
Therefore, the quantity of milk in the third container is 9 litres.
Total volume of the new mixture = 26 + 9 = 35 litres
This is our required solution.

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