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 5 of 8.
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.
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.
Pradeep said:
9 years ago
Thanks a lot @Kailash Chandra.
(1)
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.
Odett said:
8 years ago
Very good explanation @Moncy.
Kabir said:
8 years ago
12 liter milk or mix. I am confused. Is this question in right mood. Please anyone explain the question.
Sridharsan said:
8 years ago
Actually, we need 12 ltrs of milk, here where is 12 ltr of milk, 6+6=12 (it is a mix, not purely milk).
Please explain in detail.
Please explain in detail.
Sravani said:
7 years ago
So in this problem,
5/8 is taken as the total mixture is in the ratio 3:5(water:milk).
so as we are calculating for milk quantity in the aligation process, the milk quantity is according to ratio 5/3+5=5/8.
Hope you understand this.
5/8 is taken as the total mixture is in the ratio 3:5(water:milk).
so as we are calculating for milk quantity in the aligation process, the milk quantity is according to ratio 5/3+5=5/8.
Hope you understand this.
Nani said:
7 years ago
Nice explanation, thanks a lot @Vivek Kumar.
Guru Prasad said:
6 years ago
Alternate method:
-
CAN:1---> 25% water and the remaining 75% milk.
CAN:2---> 50% water and 50% milk.
Given ratio is 3:5. since only the quantity of milk is to be estimated therefore there is 5/8 of milk present in the mixture. converting this into percentage it is 62.50%.
By using allegation:-
{75% = M & 50% = N and D = 62.50%}--------> General Assumption.
M - D = 75% - 62.50%
= 12.50%.
D - N = 62.50% - 50%,
= 12.50%.
(M - D) : (D - N) = 1 : 1.
Therefore the quantity of milk to be mixed from each of the containers in order to 12 litres of milk is;
(1/2) * 12
= 6 litres. since the obtained ratio is 1:1 therefore from container-1 it is 6 litres and from container-2 it is also 6 litres.
-
CAN:1---> 25% water and the remaining 75% milk.
CAN:2---> 50% water and 50% milk.
Given ratio is 3:5. since only the quantity of milk is to be estimated therefore there is 5/8 of milk present in the mixture. converting this into percentage it is 62.50%.
By using allegation:-
{75% = M & 50% = N and D = 62.50%}--------> General Assumption.
M - D = 75% - 62.50%
= 12.50%.
D - N = 62.50% - 50%,
= 12.50%.
(M - D) : (D - N) = 1 : 1.
Therefore the quantity of milk to be mixed from each of the containers in order to 12 litres of milk is;
(1/2) * 12
= 6 litres. since the obtained ratio is 1:1 therefore from container-1 it is 6 litres and from container-2 it is also 6 litres.
(2)
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