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 12 of 20.
VIUAY said:
10 years ago
I totally can't understand please explain in easiest way.
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.
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.
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%.
Subhankar said:
1 decade ago
(bigger - smaller)/(2xbigger).
Venugopal said:
1 decade ago
@Victor.
Why did you divide syrup into 5 parts?
Why did you divide syrup into 5 parts?
Preeti rani dass said:
1 decade ago
Can you explain with the other method?
Ashwin said:
1 decade ago
Hey @Kiran I didn't understand you.
How you get 60% and 40%?
How you get 60% and 40%?
Dinesh said:
1 decade ago
Before going to shortcuts I explain some known facts about this question.
1. Only water is added and no effect on syrup.
2. So think like how much water is added so that mixture is 1:1.
Lets start my shortcuts:
Water:Syrup 3:5.
After mixing water 1:1.
We know syrup has no loss and no gain so we first make part of syrup is 5. Hence we multiply by 5 in 1:1, we get 5:5.
Finally we see:
Before 3:5.
After 5:5.
Clearly we see that two part of water is added.
Hence amount of water added as new solution is gives answer.
2/10 = 1/5.
Trick is based on how much you think and how much you understand.
1. Only water is added and no effect on syrup.
2. So think like how much water is added so that mixture is 1:1.
Lets start my shortcuts:
Water:Syrup 3:5.
After mixing water 1:1.
We know syrup has no loss and no gain so we first make part of syrup is 5. Hence we multiply by 5 in 1:1, we get 5:5.
Finally we see:
Before 3:5.
After 5:5.
Clearly we see that two part of water is added.
Hence amount of water added as new solution is gives answer.
2/10 = 1/5.
Trick is based on how much you think and how much you understand.
Dinesh said:
1 decade ago
Before going to shortcuts I explain some known facts about this question.
1. Only water is added and no effect on syrup.
2. So think like how much water is added so that mixture is 1:1.
Lets start my shortcuts:
Water:Syrup 3:5.
After mixing water 1:1.
We know syrup has no loss and no gain so we first make part of syrup is 5. Hence we multiply by 5 in 1:1, we get 5:5.
Finally we see:
Before 3:5.
After 5:5.
Clearly we see that two part of water is added.
Hence amount of water added as new solution is gives answer.
2/10 = 1/5.
Trick is based on how much you think and how much you understand.
1. Only water is added and no effect on syrup.
2. So think like how much water is added so that mixture is 1:1.
Lets start my shortcuts:
Water:Syrup 3:5.
After mixing water 1:1.
We know syrup has no loss and no gain so we first make part of syrup is 5. Hence we multiply by 5 in 1:1, we get 5:5.
Finally we see:
Before 3:5.
After 5:5.
Clearly we see that two part of water is added.
Hence amount of water added as new solution is gives answer.
2/10 = 1/5.
Trick is based on how much you think and how much you understand.
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