Mixtures And Alligations - MCQ 1


20 Questions MCQ Test Quantitative Aptitude for Competitive Examinations | Mixtures And Alligations - MCQ 1


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QUESTION: 1

Vikram covered 180 km distance in 10 hours. The first part of his journey he covered by Car, then he hired a Rickshaw. The speed of the car and rickshaw is 25 kmph and 15 kmph respectively. The ratio of the distances covered by the car and the rickshaw is

Solution:

Answer – C. 7:5 Explanation : Average Speed = 180/10 = 18kmph 15………………….25
…………18…………..
7…………………….3
The ratio of time taken by rickshaw to car = 7:3 The ratio of distances covered by rickshaw to car = 7 * 15 : 3 * 25 = 7:5

QUESTION: 2

A mixture of wheat is sold at Rs.3 per Kg. This mixture is formed by mixing the Wheat of Rs.2.10 per kg and Rs.2.52 per kg. What is the ratio of price of cheaper to the costlier quality in the mixture if the profit of 25% is being earned

Solution:

Answer – A.2:5 Explanation : Selling Price = x + 25*x/100 = 3; x = 2.4 210………………….252
…………240…………..
12…………………….30
2:5

QUESTION: 3

From the 50 liters of a chemical solution, 5 liters of chemical solution is taken out and after it, 5 liters of water is added to the rest amount of chemical solution. Again 5 liters of chemical solution and water is drawn out and it was replaced by 5 liters of water. If this process is continued similarly for the third time, the amount of chemical solution left after the third replacement

Solution:

Answer – C.36.45 Explanation : 50 * 45/50 * 45/50 *45/50 = 36.45L

QUESTION: 4

 From a container of milk, which contains 200 liters of milk, the seller replaces each time with water when he sells 40 liters of milk(or mixture). Every time he sells out only 40 liters of milk(or mixture). After replacing the milk with water 4th time, the total amount of water in the mixture is 

Solution:

Answer – B. 81.92L Explanation : The amount of Milk left after 4 operations  = 200(1-40/100) = 200 *(4/5) = 200 * 256/625 = 81.92L; Amount of water = 200 – 81.92 = 118.08L

QUESTION: 5

A jar was full with Milk. A person used to draw out 20% of the Milk from the jar and replaced it with water. He has repeated the same process 4 times and thus there was only 512 gm of milk left in the jar, the rest part of the jar was filled with the water. The initial amount of milk in the jar was: 

Solution:

Answer – D. 1.25 kg Explanation : Shortcut: 512 = x(1-1/5) x = 1.25 kg

QUESTION: 6

 From a container of Milk, a thief has stolen 15 liters of milk and replaced it with same quantity of water. He again repeated the same process. Thus in three attempts, the ratio of Milk and water became 343:169. The initial amount of Milk in the container was:

Solution:

Answer – D.120 litre Explanation : Milk(Left) = 343 Milk(Initial amount) = 512 343x = 512x(1 – 15/y) (1-15/y) = 7/8 y = 120 litre

QUESTION: 7

 The ratio of Solution “A” and Solution “B” in the container is 3:2 when 10 liters of the mixture is taken out and is replaced by the Solution “B”, the ratio become 2:3. The total quantity of the mixture in the container is:

Solution:

Answer – C.30L Explanation : Initial = 3:2 ; After replacement = 2:3 2/3 = (1 – 10/n) n = 30L

QUESTION: 8

 From a container, 6 liters Solution “A” was drawn out and was replaced by water. Again 6 liters of the mixture was drawn out and was replaced by the water. Thus the quantity of Solution “A” and water in the container after these two operations is 9:16. The quantity of the mixture is:

Solution:

Answer – D.15L Quantity of solution “A” = x(1-6/x)² Solution “A” : Water = 9 : 16 Solution “A” : Solution “A” + water = 9:25 x(1-6/x)²/x = 9/25 x = 15L

QUESTION: 9

The diluted Milk contains only 8 liters of Milk and the rest is water. A new mixture whose concentration is 30%, is to be formed by replacing Milk. How many liters of the mixture shall be replaced with pure Milk if there was initially 32 liters of water in the mixture?

Solution:

Answer – D. 5 litre Explanation : Milk : Water 8 : 32 => 1:4
Original Ratio = 20%:80% Required Ratio = 30%:70% Original Ratio(water) = 80% Required Ratio(water) = 70% 7/8 = (1-x/40) x = 5 litre

QUESTION: 10

In a school, the average weight of boys in a class is 30 kg and the average weight of girls in the same class is 20kg. If the average weight of the whole class is 23.25 kg, what could be the possible strength of boys and girls respectively in the same class?

Solution:

Answer – B. 13 and 27 Explanation : 20…………………….30
…………23.25…………..
6.75…………………….3.25
Total number of boys and Total number of girls = 13 and 27

QUESTION: 11

A Container contains 192 liter of Milk. A seller draws out x% of Milk and replaced it with the same quantity of water. He repeated the same process for 3 times. And thus Milk content in the mixture is only 81 liter. Then how much percent he withdraw every time?

Solution:

Answer – 5. 25% Explanation : 81 = 192(1-x/100)³ x = 25

QUESTION: 12

A Jar contains 30 liters mixture of Milk and Water in the ratio of x:y respectively. When 10 liter of the mixture is taken out and replaced it water, then the ratio becomes 2:3. Then what is the initial quantity of Milk in the Jar?

Solution:

Answer – 3. 18 Liter Explanation : x+y =30 (x-10*x/x+y)/ (y-10*y/(x+y) + 10) = 2/3 2x-4/3y = 20 x =18

QUESTION: 13

A Container contains ‘X’ Liters of Milk. A thief stole 50 Liters of Milk and replaced it with the same quantity of water. He repeated the same process further two times. And thus Milk in the container is only ‘X-122’ liters. Then what is the quantity of water in the final mixture?

Solution:

Answer –1. 122 Liter Explanation : X-122 = X(1-50/X)³
X = 250 Liter Milk = 250-122 = 128 Water = 122

QUESTION: 14

A Jar contains 100 liters of Milk a thief stole 10 liter of Milk and replaced it with water. Next, he stole 20 liter of Milk and replaced it with water. Again he stole 25 liter of Milk and replaced with water. Then what is the quantity of water in the final mixture?

Solution:

Answer – 4. 46 Liter Explanation : Solution: Milk = 100*90/100*80/100*75/100 = 54 Water = 100-54 = 46

QUESTION: 15

In a 250 liter of a mixture of Milk and Water, Water is X%. The milkman sold 50 liters of the mixture and replaced same quantity with water. If the percent of Milk in final mixture is 64%, then what is the percentage of Milk in the initial mixture?

Solution:

Answer – 5. 80% Explanation : Milk = 250*(100-x/100) 50 liters replaced then 250*(100-x/100) – 50*(100-x/100) = 64% of 250 X = 20%
Milk = 80%

QUESTION: 16

A jar contains ‘x’ liters of Milk, a seller withdraws 25 liter of it and sells it at Rs.20 per liter. He then replaces it water. He repeated the process total three times. Every time while selling he reduces selling price by Rs.2. After this process Milk left in the mixture is only 108 liters so he decided to sell the entire Mixture at Rs. 15 per liter. Then how much profit did he earned if bought Milk at Rs.20 per liter?

Solution:

Seller sells Milk at Rs.20,18 and 16 respectively for three times
= 25*(20+18+16) = 1350
108 = x(1-25/100) 3
x =256 liter
He sold entire 256 at Rs.15 =256*15 = 3840
Cost price = 256*20 = 5120
profit = 5190-5120 = 70

QUESTION: 17

‘X’ Liters of the mixture contains Milk and Water in the ratio 4:3. If 13 liters of Water is added then the ratio becomes 1:1. Then what is the final quantity of water in the mixture?

Solution:

Answer – 2. 52 Explanation : 4x/3x+13 = 1 x = 13 Water = 3x+13 = 39+13 = 52

QUESTION: 18

A Jar contains 200 liters of Milk a thief stole ‘X’ liters of Milk and replaced it with water. Next, he stole 40 liters of Milk and replaced it with water. Again he stole 50 liters of Milk and replaced with water. If the quantity of water in the final mixture is 92 liters. Then what is the value of X?

Solution:

Answer –3. 20 Liter Explanation : Milk = 200-92 =108 108 = 200*(200-x)/200*160/200*150/200 x = 20 Liter

QUESTION: 19

From a container, a thief has stolen 10 liters of Milk and replaced with the same quantity of water. He repeated the process for three times, then the ratio of Milk to water became 343:169.The initial amount of Milk in the container is?

Solution:

Answer – 1. 80 liter 343x = 512x(1-10/y) y = 80

QUESTION: 20

A Jar contains a mixture of Milk and Water 18 and 12 Liters respectively.
When ‘x’ liter of the mixture is taken out and replaced with the same quantity of Water, then the ratio of Milk and Water becomes 2:3. Then what is the quantity of Water in final Mixture?

Solution:

Answer – 3. 18 Liter Explanation : (18-x*18/30)/(12- x*12/30+x) =2/3 x = 10 Water = 12+3/5*10 = 18

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