Aptitude - Alligation or Mixture - Discussion
Discussion Forum : Alligation or Mixture - General Questions (Q.No. 1)
1.
A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
Answer: Option
Explanation:
Suppose the vessel initially contains 8 litres of liquid.
Let x litres of this liquid be replaced with water.
| Quantity of water in new mixture = |  |
3 - | 3x | + x |  |
litres |
| 8 |
| Quantity of syrup in new mixture = | |
5 - | 5x | |
litres |
| 8 |
 |
|
3 - | 3x | + x | |
= | |
5 - | 5x | |
| 8 | 8 |
5x + 24 = 40 - 5x
10x = 16
| x = |
8 | . |
| 5 |
| So, part of the mixture replaced = | |
8 | x | 1 | |
= | 1 | . |
| 5 | 8 | 5 |
Discussion:
198 comments Page 13 of 20.
VCillusion said:
10 years ago
For 62.5% water, to get to 50%, 12.5 must go which is exactly 20% of 62.5.
Syrup is to water = 3 : 5.
% water in mixture = 5/8*100 = 62.5%.
Desired % of water = 1/2*100 = 50%.
Difference = 62.5-50 = 12.5%.
To get 50% of water the 12.5% must go.
Hence Formula = Difference/Current Water in Mixture.
= 12.5/62.5 = 1/5 = 20 %.
5 syrup parts of 8 = 62.5% syrup, to get to 50%, 12.5 must go which is exactly 20% of 62.5.
Syrup is to water = 3 : 5.
% water in mixture = 5/8*100 = 62.5%.
Desired % of water = 1/2*100 = 50%.
Difference = 62.5-50 = 12.5%.
To get 50% of water the 12.5% must go.
Hence Formula = Difference/Current Water in Mixture.
= 12.5/62.5 = 1/5 = 20 %.
5 syrup parts of 8 = 62.5% syrup, to get to 50%, 12.5 must go which is exactly 20% of 62.5.
Vivek said:
10 years ago
Let be x liters of mixture.
From equation quantity of pure liquid = x*(1-y/x)^n.
Where why is quantity of water used.
N is no. of times water replaces the liquid.
x liters of mixture and why liters of water final quantity of pure liquid = 1/2*x.
So from equation 1/2*x = 5/8*x(1-y/x).
Where 5/8*x is the initial quantity of syrup.
We need to find out y/x.
So, 1/2 = 5/8*(1- y/x).
1-(y/x) = 4/5.
y/x = 1-(4/5).
y/x = 1/5.
From equation quantity of pure liquid = x*(1-y/x)^n.
Where why is quantity of water used.
N is no. of times water replaces the liquid.
x liters of mixture and why liters of water final quantity of pure liquid = 1/2*x.
So from equation 1/2*x = 5/8*x(1-y/x).
Where 5/8*x is the initial quantity of syrup.
We need to find out y/x.
So, 1/2 = 5/8*(1- y/x).
1-(y/x) = 4/5.
y/x = 1-(4/5).
y/x = 1/5.
VIUAY said:
10 years ago
I totally can't understand please explain in easiest way.
Ramakrishna said:
10 years ago
@Chacha chodary.
I did not get can you explain clearly?
I did not get can you explain clearly?
Ram said:
10 years ago
What if ratios are 2:1:2?
Vish said:
10 years ago
Quantity of syrup = x(1-y/x) raise to n, n = 2.
Here, 8(1-3/5) raise go 2.
= 4/5.
So quantity of water = 1-4/5 = 1/5.
Here, 8(1-3/5) raise go 2.
= 4/5.
So quantity of water = 1-4/5 = 1/5.
Vinod said:
10 years ago
Water : Syrup. 3:5.
Water = 3x.
Syrup = 5x.
Volume = 8x.
Why liters mixture withdrawn and replaced with water.
Applying the condition.
3x-3/8y+y = 5x-5/8y.
16x = 10y.
8x = 5y.
y = 8x/5.
y = Volume/5.
Water = 3x.
Syrup = 5x.
Volume = 8x.
Why liters mixture withdrawn and replaced with water.
Applying the condition.
3x-3/8y+y = 5x-5/8y.
16x = 10y.
8x = 5y.
y = 8x/5.
y = Volume/5.
Neeru said:
10 years ago
I think density of both ingredient is of some importance. That can be further related to concentration.
Jitendra said:
9 years ago
Let the volume of the mixture be 8 litres, in which 3 litre is water and 5 litres is syrup.
Now add 2 litre of water in the mixture, the volume becomes 10 litre and the ratio becomes 1:1.
Since the earlier mixture was 8 litre in volume.
Therefore we have to subtract 2 litres from the new mixture, so as it becomes 8 litres.
Now calculate how much part of the mixture was subtracted from the new mixture i.e. (2/10 or 1/5).
Now add 2 litre of water in the mixture, the volume becomes 10 litre and the ratio becomes 1:1.
Since the earlier mixture was 8 litre in volume.
Therefore we have to subtract 2 litres from the new mixture, so as it becomes 8 litres.
Now calculate how much part of the mixture was subtracted from the new mixture i.e. (2/10 or 1/5).
Raj said:
9 years ago
Actually the correct answer is 8/5.
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