Basic Concept and Quiz on Mixture and Alligation

Mixture: Mixing of two or more than two type of quantities gives us a mixure.
Quantities of these elements can be expressed as percentage or ratio.
(1) Percentage:- (20% of sugar in water)

(2)Fraction:- A solution of sugar and water such that
  (sugar : water = 1:4)



Alligation: Alligation is a rule which is used to solve the problems related to mixture and its ingredient.It is the rule that enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of desired price.
Alligation Rule:-
When two elements are mixed to make a mixture and one of the elements is cheaper and other one is costlier then




Here Mean Price is CP of mixture per unit quantity.
Above rule can be written as,










Cheaper Quantity : Costlier Quantity = (D – M) : (M – C)

Trick: 
If n different vessels of equal size are filled with the mixture of P and Q in the ratio p1 : q1, p2 : q2, ……, pn : qn and content of all these vessels are mixed in one large vessel, then






Quant Quiz on mixture and Allegation:-
1. A can contains a mixture of two liquids A and B in the ratio 7:5 when 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many litres of liquid A was contained by the can initially?
A.28 litres
B.21 litres
C.45 litres
D.36 litres

2.A man travelled a distance of 90Km in 9 hours partly on foot at 8 kmph and partly on bicycle at 17 kmph. Find the distance travelled on foot.
A.46 km
B.56 km
C.62 km
D.52 km

3.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 container so as to get 12 litres of milk such that the ratio of water to milk is 3:5?
A.6 litres
B.1 litres
C.8 litres
D.7 litres

4. In what ratio must a person mix three kinds of wheat costing him Rs 1.20,Rs 1.44 and Rs 1.74 per Kg so that the mixture may be worth Rs 1.41 per Kg?
A.11:77:7
B.25:45:8
C.27:23:6
D.11:45:7

5.A painter mixes blue paint with white paint so that the mixture contains 10% blue paint.In a mixture of 40 litres paint how many litres blue paint should be added so that the mixture contains 20% of blue paint.
A. 2.5 litres
B. 4litres
C. 5litres
D.2 litres

Answers
1.       (B) Let initially contained 7x & 5x
So, 
         (7x-9/12*7)/(5x-9/12*5+9)=7/9

        (12x-9)/(60x+63)=1/9

         x=3
Required Quantity = 7x = 7*3=21 litres

2.       (B) Average Speed =  90/9=10kmph
So,         
By Rule of Allegations 
















Required Distance = 7*8=56 km

3.       (A) Milk in 1st can = ¾
Milk in IInd can = ½
Milk in Resultant mixture = 5/8
So,

















1 + 1 = 12
2 = 12
1 = 6 liter

4.       (A) In first case, We take 1. 20, 1.44 & 1. 41

So,

















                                             1:7
In second case, We take 1.20, 1. 74 & 1. 41
so,

      















                                            11 : 7

Since     I : II                        = 1.7
I : III                      = 11 : 7
So,          I : II : III               = 11 : 77 : 7

5.       (C) Percentage of blue point, in pure Blue point =100%

So,

                                 















       8 : 1
Since 8 = 40  
1 = 5 liters




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