New : Electrical Engineering
For premium access

 Home Aptitude Gen.Knowledge English/Verbal Engineering Reasoning

 Home->Aptitude->Alligation or Mixture ->Formula/Rule 15

 Alligation or Mixture :-
 ::Important Formulas ::Examples

Direct Formula / Rule 15 :

• Theorem: Ajar contains a mixture of two liquids A and B in the ratio a : b. When L litres of the mixture is taken out and P litres of liquid B is poured into the jar, the ratio becomes x : y. Then the amount of liquid A, contained in the jar, is given by  = [ L(y/x - b/a)+P(1 + b/a) X (x/y X a/b) ] litres (a/b - b/a X x/y)+(1 - x/y)

and the amount of liquid B in the jar is given by  = [ L(y/x - b/a)+P(1 + b/a) X (x/y) ] litres (a/b - b/a X x/y)+(1 - x/y)

• Example :

• Ajar contains a mixture of two liquids A and B in the ratio 4 : 1. When 10 litres of the mixture is taken out and 10 litres of liquid B is poured into the jar, the ratio becomes 2 : 3. How many litres of liquid A was contained in the jar?

• Detail Method :
Let the quantity of mixture in the jar be 5x litres. Then  = 4x - 10 ( 4 ) x - 10 ( 1 ) + 10 = 2 : 3 4 + 1 4 + 1
or, 4x - 8 : x - 2 + 10 = 2 : 3  Or, 4x - 8 = 2 x + 8 3
So x = 4
Then quantity of A in the mixture = 4x = 4 x 4 = 16 litres.

• Ailigation Method :
Method I.
In original mixture, % of liquid B  = 1 X 100 = 20% 4 + 1
In the resultant mixture, % of liquid B  = 3 X 100 = 60% 2 + 3
Replacement is made by the liquid B, so the % of B in second mixture = 100%
Then by the method of Alligation:  20% 60% 100% 40% 40%
Ratio in which first and second mixtures should be added is 1 : 1. What does it imply? It simply implies that the reduced quantity of the first mixture and the quantity of mixture B which is to be added are the same.
Total mixture = 10 + 10 = 20 litres.  and liquid A = 20 X 4 = 16 litres. 5
Method II.
The above method is explained through percentage. Now, method II will be explained through fraction.  Fraction of B in original mixture = 1 5
Fraction of B in second mixture (liquid B) = 1  Fraction of B in resulting mixture = 3 5
So,  1/5 3/5 1 2/5 2/5
Thus, we see that the original mixture and liquid B are mixed in the same ratio. That is, if 10 litres of liquid B is added then after taking out 10 litres of mixture from the jar, there should have been 10 litres of mixture left. So, the quantity of mixture in the jar = 10 + 10 = 20 litres
Total mixture = 10 + 10 = 20 litres.  and quantity of A in the jar = 20 X 4 = 16 litres. 5

• Quicker Method : Here you can use direct formula :
Amount of liquid A contained in the jar  = [ 10(3/2 - 1/4)+10(1 + 1/4) X (2/3 X 4/1) ] (4 - 1/4 X 2/3)+(1 - 2/3)
 = 25/2 + 25/2 X 2/3 X 4/1 23/6 + 1/3
= 8 X 2 = 16 litres.

Exercise :
1. A vessel contains mixture of liquids A and B in the ratio 3 : 2. When 20 litres of the mixture is taken out and replaced by 20 litres of liquid B, the ratio changes to 1 : 4. How many litres of liquid A was there initially present in the vessel?
2. A can contains a mixture of two liquids in proportion 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the proportion of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?
3. Ajar contains a mixture of two liquids A and B in the ratio 3 : 1. When 15 litres of the mixture is taken out and 9 litres of liquid B is poured into the jar, the ratio becomes 3 : 4. How many litres of liquid A was contained in the jar?
4. Answers : 1 = 18 litres,   2 = 21 litres,   3 = 27 litres

 Prev.Rule.. Next Rule..