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1. Alligation
It 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. Suppose a container contains x of liquid from which y units are taken out and replaced by water. After n operations, the quantity of pure liquid = [x(1−y/x)n] units.
4. Rule of Alligation
If two ingredients are mixed, then
(Quantity of cheaper/Quantity of dearer)=(C.P. of dearer - Mean Price)/(Mean price - C.P. of cheaper)
5. => (Cheaper quantity) : (Dearer quantity) = (d - m) : (m - c)
Solved Examples
1. A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container? | |
A. 26 litres | B. 29.16 litres |
C. 28 litres | D. 28.2 litres |
Answer : Option B
Explanation :
Assume that a container contains x of liquid from which y units are taken out and replaced
=[x(1−y/x)n]
Hence milk now contained by the container = 40(1−4/40)3=40(1−1/10)3
40×9/10×9/10×9/10=(4×9×9×9)/100=29.16
2. A jar full of whiskey contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohols and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is | |
A. 43 | B. 34 |
C. 32 | D. 23 |
Answer : Option D
Explanation :
Concentration of alcohol in 1st Jar = 40%
Concentration of alcohol in 2nd Jar = 19%
After the mixing, Concentration of alcohol in the mixture = 26%
By the rule of alligation
Hence ratio of 1st and 2nd quantities = 7 : 14 = 1 : 2
3. In what ratio should rice at Rs.9.30 per Kg be mixed with rice at Rs. 10.80 per Kg so that the mixture be worth Rs.10 per Kg ? | |
A. 7 : 8 | B. 8 : 7 |
C. 6 : 7 | D. 7 ; 6 |
Answer : Option B
Explanation :
By the rule of alligation, we have
Required ratio = .8 : .7 = 8 : 7.
4. In what ratio must water be mixed with milk costing Rs.12 per litre in order to get a mixture worth of Rs.8 per litre? | |
A. 1 : 3 | B. 2 : 2 |
C. 1 : 2 | D. 3 : 1 |
Answer: Option C
Explanation:
By the rule of alligation, we have
Required Ratio = 4 : 8 = 1 : 2
5. In 1 kg mixture of iron and manganese 20% of manganese. How much iron should be added so that the proportion of manganese becomes 10% | |
A. 1.5 Kg | B. 2 Kg |
C. .5 Kg | D. 1 Kg |
Answer : Option D
Explanation :
By the rule of alligation, we have
=> Quantity of the mixture : Quantity of iron = 10 : 10 = 1 : 1
Given that Quantity of the mixture = 1 Kg
Hence Quantity of iron to be added = 1 Kg
6. A trader has 1600Kg of sugar. He sells a part at 8% profit and the rest at 12% profit. If he gains 11% on the whole , find the quantity sold at 12%. | |
A. 1200 Kg | B. 1400 Kg |
C. 1600 Kg | D. 800 Kg |
Answer : Option A
Explanation :
By the rule of alligation, we have
=>Quantity of part1 : Quantity of part2 = 1 : 3
Given that total quantity = 1600 Kg
Hence quantity of part2 (quantity sold at 12%) = 1600×3/4=1200
7. How many litres of water must be added to 16 liters of milk and water contains 10% water to make it 20% water in it | |
A. 4 litre | B. 2 litre |
C. 1 litre | D. 3 litre |
Answer : Option B
Explanation :
By the rule of alligation, we have
=> Quantity of water : Quantity of the mixture = 10 : 80 = 1 : 8
Here Quantity of the mixture = 16 litres
=> Quantity of water : 16 = 1 : 8
Quantity of water = 16×1/8=2 litre
8. A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold at 18% profit is | |
A. 300 | B. 400 |
C. 600 | D. 500 |
Answer : Option C
Explanation :
By the rule of alligation,we have
=> Quantity of part1 : Quantity of part2 = 4 : 6 = 2 : 3
Total quantity is given as 1000Kg
So Quantity of part2 (Quantity sold at 18% profit) = 1000×3/5=600Kg
9. Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety of tea in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, what is the price of the third variety per kg ? | |
A. Rs.182.50 | B. Rs.170.5 |
C. Rs.175.50 | D. Rs.180 |
Answer : Option C
Explanation :
Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed in the ratio 1 : 1
So their average price = (126+135)2=130.5
Hence let's consider that the mixture is formed by mixing two varieties of tea.
one at Rs. 130.50 per kg and the other at Rs. x per kg in the ratio 2 : 2, i.e.,
1 : 1. Now let's find out x.
By the rule of alligation, we can write as
(x - 153) : 22.5 = 1 : 1
=>x - 153 = 22.50
=> x = 153 + 22.5 = 175.5
10. A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5? | |
A. 5litres, 7 litres | B. 7litres, 4 litres |
C. 6litres, 6 litres | D. 4litres, 8 litres |
Answer : Option C
Explanation :
Let cost of 1 litre milk be Rs.1
Milk in 1 litre mix in 1st can = 3/4 litre
Cost Price(CP) of 1 litre mix in 1st can = Rs.3/4
Milk in 1 litre mix in 2nd can = 1/2 litre
Cost Price(CP) of 1 litre mix in 2nd can = Rs.1/2
Milk in 1 litre of the final mix=5/8
Cost Price(CP) of 1 litre final mix = Rs.5/8
=> Mean price = 5/8
By the rule of alligation, we can write as
=> mix in 2nd can :mix in 1st can = 1/8 : 1/8 = 1:1
ie, from each can, 12×12=6 litre should be taken
1. What is the concept of mixture and alligation in quantitative aptitude? |
2. How is mixture and alligation related to the Civil Service Examination? |
3. What are some common applications of mixture and alligation in real life? |
4. How can one approach solving mixture and alligation problems in the quantitative aptitude section? |
5. Are there any shortcuts or tricks to solve mixture and alligation problems quickly? |
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