# Mixtures and Alligations - Formulas, Tricks, Questions and Solved Examples - Quantitative Aptitude Quiz

## Formulas and Quick Tricks for Mixtures and Alligations

1. Alligation: Alligation is the rule which enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of a specified price.
2. Mean Price: Mean price is the cost price of a unit quantity of the mixture.
3. Rule of Alligation: If two ingredients are mixed, then: (Quantity of cheaper / Quantity of dearer) = (CP of dearer - Mean Price / Mean price - CP of cheaper)
4. If the number of quantities in two groups be n1 and n2 and their average is x and y respectively, the combined average is (n1x+n2y) / (n1+ n2)
5. The average of n quantities is equal to x. When a quantity is removed, the average becomes y. The value of the removed quantity is n(x-y) + y
6. The average of n quantities is equal to x. When a quantity is added, the average becomes y. The value of the new quantity is n(y-x) + y

## Questions and Solved Examples on Mixtures and Alligations

1. A Jar contains 30 litres mixture of Milk and Water in the ratio of x:y respectively. When 10 litre 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?
A. 12 Litres
B. 15 Litres
C. 18 Litres
D. 20 Litres

C. 18 Litres
x+y =30
(x-10*x/x+y)/ (y-10*y/(x+y) + 10) = 2/3
2x-4/3y = 20
x = 18
3. A Container contains ‘X’ litres of Milk. A thief stole 50 litres 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’ litres. Then what is the quantity of water in the final mixture?
A. 122 Litres
B. 124 Litres
C. 128 Litres
D. 250 Litres

A. 122 Litres
X-122 = X(1-50/X)³
X = 250 Litres
Milk = 250-122 = 128
Water = 122 Aptitude Test & Logical Reasoning Test

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5. A Jar contains 100 litres of Milk a thief stole 10 litre of Milk and replaced it with water. Next, he stole 20 litre of Milk and replaced it with water. Again he stole 25 litre of Milk and replaced with water. Then what is the quantity of water in the final mixture?
A. 46 Litres
B. 50 Litres
C. 54 Litres
D. 55 Litres

C. 54 Litres
Milk = 100*90/100*80/100*75/100 = 54
Water = 100-54 = 46
7. In a 250 litre of a mixture of Milk and Water, Water is X%. The milkman sold 50 litres 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?
A. 20%
B. 40%
C. 60%
D. 80%

D. 80%
Milk = 250*(100-x/100)
50 litres replaced then,
250*(100-x/100) – 50*(100-x/100) = 64% of 250
X = 20%
Milk = 80%
9. A jar contains ‘x’ litres of Milk, a seller withdraws 25 litre of it and sells it at Rs.20 per litre. 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 litres so he decided to sell the entire Mixture at Rs. 15 per litre. Then how much profit did he earned if bought Milk at Rs.20 per litre?
A. Rs. 50
B. Rs. 70
C. Rs. 90
D. Rs. 100

B. Rs.70
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 litre
He sold entire 256 litres at Rs.15 =256*15 = 3840
Cost price = 256*20 = 5120
Profit = 5190-5120 = 70
11. Shailesh covered 180 kms 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:
A. 7:9
B. 7:5
C. 7:3
D. 7:2

B. 7:5
Average Speed = 180/10 = 18 kmph
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
13. 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?
A. 2:1
B. 2:3
C. 2:5
D. 2:7

C. 2:5
Selling Price = x + 25*x/100 = 3; x = 2.4
210…………………252
…………240…………
12……………………30
Hence, Ratio = 2:5
15. From a container of milk, which contains 200 litres of milk, the seller replaces each time with water when he sells 40 litres of milk(or mixture). Every time he sells out only 40 litres of milk(or mixture). After replacing the milk with water 4th time, the total amount of water in the mixture is
A. 75.82L
B. 81.92L
C. 85.28L
D. 87.45L

B. 81.92L
The amount of Milk left after 4 operations = 200(1-40/100)4
= 200 *(4/5)4= 200 * 256/625 = 81.92L;
Amount of water = 200 – 81.92 = 118.08L
17. The diluted Milk contains only 8 litres of Milk and the rest is water. A new mixture whose concentration is 30%, is to be formed by replacing Milk. How many litres of the mixture shall be replaced with pure Milk if there was initially 32 litres of water in the mixture?
A. 3 litres
B. 4 litres
C. 5 litres
D. 8 litres

C. 5 litres
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 litres
19. 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 20 kg. 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?
A. 18 and 19
B. 16 and 15
C. 15 and 13
D. 13 and 27