COMPACT QUESTION (MIXTURE AND ALLIGATIONS)-1

Mixture
The new product obtained by mixing two or more ingredients in a certain ratio is called a mixture 

Mean price
The cost price of a unit quantity in the mixture is called the mean price. it will always be higher than the cost price of the cheaper quantity and the lower than the cost price of dearer quantity.

Rule of Alligation
It is the rule that enables to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of desired price.
Let the cost price of a unit of cheaper article is Rs c and that of a unit of costly article is Rs d and the average (mean) price of mixture is Rs m, then
(Quantity of cheaper article)/(Quantity of costly article)
= (Cos price of a unit of a costly article - Mean price)/(Mean price - Cost price of a unit of a cheaper article )
The above relation can be represented pictorically as 
    Cheaper price (c)               Dearer price (d)
               \                                   /
                           Mean Price(m)
                /                                 \
        (d - m)                          (m - c)
Hence, Quantity of cheaper/Quantity of dearer
= (d- m)/(m - c)
This method is also called as cross-section method.

1) In a mixture of 60 litres , the ratio of ethanol to ether is 4:1. The quantity of ether to be added to the mixture to make this ratio 2:1 will be
a)  10 b) 12 c) 18  d) 24 

2) The price of a variety of a commodity is Rs5 per kg and that of another is Rs8 per kg. The ratio in which the two varieties should be mixed, so that the price is Rs7 per kg will be 
a) 1:2 b) 2:1  c) 3:1 d) 8:5 

3) How many kilogram of rice costing Rs18.30 per kg must be mixed with 126 kg of rice costing Rs8.55 per kg so that 20% may gained by selling the mixture at Rs 14.40 per kg?
a) 55 kg b) 69 kg  c) 84 kg  e) 75 kg

Important formula/tricks 
1) A container initially contain 'x' units of a liquid. If 'a' unit of liquid is taken out and it is filled with 'a' unit of water repeatedly upon n times , then the final quantity of the original liquid in the container is given as 
[x(1- a/x)ⁿ] units.

2) A container has milk and water (or any two ingredients ) in the ratio a:b and second container has milk and water in the ratio c:d. If equal quantities of both the mixtures are emptied into a third container , then the ratio of the milk to water in third container is 
[a/(a+ b) + c/(c+ d)]: [b/a+ b) + d/(c+ d)]

1) A container contains 40 litre of milk. 4 litre of milk was taken out and replaced by same amount of water from this container . This process was further repeated two times. how much milk is now there in the container?
a) 28 b) 27.16 c) 29.16 d) 31.25

2) Two containers have milk and water in the ratio 2:1 and 3:1, respectively. If equal quantities of both containers are emptied into a bigger container, then find the ratio of milk to water in bigger container.
a)  5:1 b) 15:16 c) 6:5 d) 17:7

EXERCISE - A
1) If 5 kg of salt cosisting Rs5/kg and 3 kg of salt costing of Rs4/kg are mixed, find the average cost of the mixture per kg
a) 4.5 b) 4.625 c) 4 75 d) 4.125 e) 4.25

2) two types of oils having the rates of Rs 4/kg and Rs 5/kg respectively are mixed in order to produce a mixture having the rate of Rs4.60/ kg. what should be the amount of the second type of oil if the amount of the first type of oil in the mixtures is 40kg
a) 75 kg b) 50 kg c) 60 kg  d) 40 kg e) none

3)  how many kilograms of sugar worth Rs3.60 per kg should be mixed with 8 kg of sugar worth Rs 4.20 per kg, such that by selling the mixture at Rs4.40 per kg. There may be a gain of 10%?
a) 6 kg  b) 3 kg c) 2 kg d) 5 kg  e) 4 kg

4) A mixture of 125 gallons of wine and water contents 20% water. how much water must be added to the mixture in order to increase the percentage of water to 25% of these new mixtur?
a) 10 gals b) 8.5 gals c) 8 gals d) 6.66 gals e) 8.33 gals 

5) Khushi lends Rs3600 on simple interest to Harsh for a period of 5 years. She lends a part of the amount at 4% intrest and the rest at 6% and receives Rs960 as the amount of interest. How much money did he lend on 4% intrest rate?
a) 2800 b) 2100 c) 2400 d) 1200 e) 1000

6) 400 students took the AMS Mock Cat in Lucknow. 60% of boys and 80% the girls cleared the cut off in the examination. If the total percentage of students qualifying is 65%, how many girls appeared in the examination ?
a) 100 b)  120 c) 150 d) 300 e)  175

7) a man purchased a cow and a calf for Rs1300. He sold the calf at a profit of 20% and the cow at a profit of 25%. In this way his total profit was 300/13%. find the cost price of the caw
a) 1100 b) 600 c) 500 d) 400 e) 800

8) The average salary per head of all employees of a company is Rs600. the average salary of 120 officers is Rs4000. If the average salary per head for head of the rest of the employees is Rs560, find the total number of workers in the company ?
a) 1020 b) 1032 c) 1050 d) 1068 e) 1080 

9) A dishonest milkman purchased milk at Rs10 per litre and mixed 5 litres of water in it. By selling the mixture at the rate of Rs10 per litres he earns a profit of 25%. The quantity of the amount of the mixture that he had was ?
a) 15 b) 20 c) 25 d) 30 e) none 

10) A cistern contains 50 litres of water. 5 litres of water is taken out of it and replaced by wine . The process is repeated again. Find the proportion of wine and water in the resulting mixture.
a) 1: 4 b) 41:50 c) 19:81 d) 81 :19 e) 50: 41 

11) In what ratio should two qualities of coffee powder having the rates of Rs47 per kg and Rs32 per kg be mixed in order to get a mixture that would have a rate of Rs37 per kg?
a) 1: 2 b) 2:1 c) 1:3 d) 3:1 e) 4:1 

12) In what ratio should water remix be mixed with soda costing Rs12 per litres so as to make a profit of 25% by selling the diluted liquid at Rs13.75 per litres?
a) 10:1 b) 11:1 c) 1:11 d) 1 2:1 e) 1: 12

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