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 9 of 20.
Ashwin said:
1 decade ago
Hey @Kiran I didn't understand you.
How you get 60% and 40%?
How you get 60% and 40%?
Preeti rani dass said:
1 decade ago
Can you explain with the other method?
Venugopal said:
1 decade ago
@Victor.
Why did you divide syrup into 5 parts?
Why did you divide syrup into 5 parts?
Subhankar said:
1 decade ago
(bigger - smaller)/(2xbigger).
RICKY said:
1 decade ago
The liquid still remains in 3:5 even after drawing off some liquid.
Now to bring it into 1:1 we will have to add 2 to 3 I mean just 40% of remaining syrup.
Now if after drawing off some liquid, the quantity of the solution is 8 litres i.e.3 litres water and 5 litres syrup we have to add 2 litres water to bring it in 1 : 1 which means 2 litres of 10 litres were removed. Which is 2/10 or 1/5 or 20%.
Now to bring it into 1:1 we will have to add 2 to 3 I mean just 40% of remaining syrup.
Now if after drawing off some liquid, the quantity of the solution is 8 litres i.e.3 litres water and 5 litres syrup we have to add 2 litres water to bring it in 1 : 1 which means 2 litres of 10 litres were removed. Which is 2/10 or 1/5 or 20%.
Vijay said:
10 years ago
Let 3x+5x = 24.....(1).
8x = 24.
x = 3 substitute in (1).
Then water is 9 and syrup is 15.
To make both equal subtract 3 from syrup and add it to water.
So, 3/15 = 1/5.
8x = 24.
x = 3 substitute in (1).
Then water is 9 and syrup is 15.
To make both equal subtract 3 from syrup and add it to water.
So, 3/15 = 1/5.
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.
VIUAY said:
10 years ago
I totally can't understand please explain in easiest way.
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.
Ramakrishna said:
10 years ago
@Chacha chodary.
I did not get can you explain clearly?
I did not get can you explain clearly?
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