Aptitude - Alligation or Mixture - Discussion
Discussion Forum : Alligation or Mixture - General Questions (Q.No. 4)
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?
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 | ||||||||
|
Mean Price
|
|
||||||
|
|
|||||||
 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 4 of 8.
Shambhu said:
9 years ago
Let x l & y l taken from can A(1:3) & can B(1:1) resp.
In new 12 of mixture (ratio 3:5).
x + y =12.
Water= 3*12/8 & milk= 5 * 12/8.
Then now, x/4 + y/2 = 3*12/8. (W)
And, 3x/4 + y/2 = 5*12/8. (M)
Solving both equations, we get;
x =6l & y = 6l.
In new 12 of mixture (ratio 3:5).
x + y =12.
Water= 3*12/8 & milk= 5 * 12/8.
Then now, x/4 + y/2 = 3*12/8. (W)
And, 3x/4 + y/2 = 5*12/8. (M)
Solving both equations, we get;
x =6l & y = 6l.
Pradeep said:
9 years ago
Thanks a lot @Kailash Chandra.
(1)
Skk said:
9 years ago
Water = X.
Milk = Y.
Can1 contains Water = X/4 and milk is = 3Y/4.
Can2 contains Water = X/2 and Milk is = Y/2.
Total water and milk ratio = 3/5.
But water and milk = X + Y = 12.
Water/milk Ratio = X/4 + X/2/3Y/4 + Y/2= 3/5.
Substitute X = 12 - y.
We will get X = 6 & Y = 6.
Milk = Y.
Can1 contains Water = X/4 and milk is = 3Y/4.
Can2 contains Water = X/2 and Milk is = Y/2.
Total water and milk ratio = 3/5.
But water and milk = X + Y = 12.
Water/milk Ratio = X/4 + X/2/3Y/4 + Y/2= 3/5.
Substitute X = 12 - y.
We will get X = 6 & Y = 6.
Nitin Garg said:
9 years ago
Let one can contain 100 litres of liquid (water + milk).
Now, in the first can, there is 25 l of water and 75 l of milk.
In the second can, there is 50 l of water and 50 l of milk.
Now let he takes y l of liquid from can 1 & y l of liquid from can 2.
Now the quantity of water in this y l of liquid will be ((25/100) y + (50/100) y) = (3/4) y.
But the quantity of water in 12 l of milk is ((3/8) * 12).
Equate (3/4) * y = (3/8) * 12.
y = 6.
So he will take 6 l of liquid from both the cans.
Now, in the first can, there is 25 l of water and 75 l of milk.
In the second can, there is 50 l of water and 50 l of milk.
Now let he takes y l of liquid from can 1 & y l of liquid from can 2.
Now the quantity of water in this y l of liquid will be ((25/100) y + (50/100) y) = (3/4) y.
But the quantity of water in 12 l of milk is ((3/8) * 12).
Equate (3/4) * y = (3/8) * 12.
y = 6.
So he will take 6 l of liquid from both the cans.
Saurabh said:
9 years ago
Can anyone explain me how "Milk in 1 litre mix in 1st can =3/4 litre come?
Dinesh said:
9 years ago
I think the questions is wrong because 12 is not only milk mixture, 12 is a total mixed mixture.
Yuhi said:
9 years ago
The ratio given is 3 : 5 water to milk means 5 parts of milk and 3 parts of water in total 8 parts (3 + 5). So mean here is 5/8 because we need to find out the milk percent.
Sabarinath S said:
9 years ago
Easy method: Take from options
1. Eliminate all answer whose sum is not 12L (here all r 12).
2. 3x/5x new ratio , take option A gives 3 * 4/5 * 8 not equal to 3 : 5.
So, b) 3 * 6/5 * 6 is 3 : 5.
1. Eliminate all answer whose sum is not 12L (here all r 12).
2. 3x/5x new ratio , take option A gives 3 * 4/5 * 8 not equal to 3 : 5.
So, b) 3 * 6/5 * 6 is 3 : 5.
Anil said:
9 years ago
See, first of all understand that the resultant mixture contain water and milk in ratio 3 : 5.
So, water concentration is 3/8 = P (resultant one).
Now we have first mixture (can) water concentration 1/4 = P1.
Similarly second mixture (can) water concentration 1/2 = P2.
Q1/Q2 = (P2 - P)/(P - P1).
Will give the answer as 1 : 1.
So, the answer is B.
So, water concentration is 3/8 = P (resultant one).
Now we have first mixture (can) water concentration 1/4 = P1.
Similarly second mixture (can) water concentration 1/2 = P2.
Q1/Q2 = (P2 - P)/(P - P1).
Will give the answer as 1 : 1.
So, the answer is B.
Cipher Gopal said:
9 years ago
@Amisha, can you explain how we get 5/8?
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