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Aptitude - Alligation or Mixture - Discussion

Discussion Forum : Alligation or Mixture - General Questions (Q.No. 4)
Alligation or Mixture
4.
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?
4 litres, 8 litres
6 litres, 6 litres
5 litres, 7 litres
7 litres, 5 litres
Answer: Option
Explanation:

Let the cost of 1 litre milk be Re. 1

Milk in 1 litre mix. in 1st can = 3 litre, C.P. of 1 litre mix. in 1st can Re. 3
4 4

Milk in 1 litre mix. in 2nd can = 1 litre, C.P. of 1 litre mix. in 2nd can Re. 1
2 2

Milk in 1 litre of final mix. = 5 litre, Mean price = Re. 5
8 8

By the rule of alligation, we have:

C.P. of 1 litre mixture in 1st can    C.P. of 1 litre mixture in 2nd can
3
4
Mean Price
5
8
1
2
1
8
1
8

Ratio of two mixtures = 1 : 1 = 1 : 1.
8 8

So, quantity of mixture taken from each can = 1 x 12 = 6 litres.
2

Discussion:
74 comments Page 8 of 8.
Parvy Govil said:   10 years ago
Let x litres of A and y litres of B is extracted x+y = 12.

Milk quantity = 1/5x+1/2y = 3/5(4/5x+1/2 y).

x = 5 litres.
y = 7 litres.
Shashi bhushan said:   10 years ago
Let x and y liters from the can to be mixed to make 12 liters of milk.

Can 1 has x/4 (water) and 3x/4 (milk).

Can 2 has y/2 (water) and y/2 (milk).

So new ratio of water to milk is.

(x/3+y/2)/(3x/4+y/2) = 3/5.....(1).

By the question.

x+y = 12.....(2).

To solve these equation.

x = 6, y = 6.
Megh said:   10 years ago
Can any one tell me how did you get 5/8?
Anu said:   10 years ago
Please somebody clarify the logic behind that question in short way.
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