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 5 of 20.
Vky said:
1 decade ago
Here x=8/5 is the amount in liters that has been added to make up 8 liters in total. This added quantity constitutes some part of the total volume. Right? So, this some part is stated as (x/8). Hope everyone's doubt on this has been cleared. => (8/ (5*8) ) =1/5.
1/5th is the part (not liters) from the total 8liters that has been added. Thank You.
1/5th is the part (not liters) from the total 8liters that has been added. Thank You.
Neel Mitra said:
8 years ago
Initially, there were 3/8 water,
We will remove 3x/18 from water and add x water [x is the qty of the liquid which was removed.]
So new water = 3/8 - 3x/8 + x
The same way we can say new syrup 5/8 - 5x/8,
So the equation will be
3/8 - 3x/8 + x = 5/8 - 5x/8,
(3 - 3x + 8x)/8 = (5-5x)/8,
3 + 5x = 5 - 5x,
10x = 2,
x = 1/5;
so 1/5 is the answer.
We will remove 3x/18 from water and add x water [x is the qty of the liquid which was removed.]
So new water = 3/8 - 3x/8 + x
The same way we can say new syrup 5/8 - 5x/8,
So the equation will be
3/8 - 3x/8 + x = 5/8 - 5x/8,
(3 - 3x + 8x)/8 = (5-5x)/8,
3 + 5x = 5 - 5x,
10x = 2,
x = 1/5;
so 1/5 is the answer.
Priyanshu Chaudhary said:
7 months ago
If we remove 1 amt of the mixture -> 5/8 amt of syrup is removed.
Let's say our ans is x -> remove x amt of mixture -> (5/8)x or syrup is removed.
for both water and syrup to be in the same amount, the syrup should be 4/8 that is 1/8 of the syrup should be removed from the mixture.
Therefore (5/8)x = 1/8 => x = 1/5 =>ANSWER.
Let's say our ans is x -> remove x amt of mixture -> (5/8)x or syrup is removed.
for both water and syrup to be in the same amount, the syrup should be 4/8 that is 1/8 of the syrup should be removed from the mixture.
Therefore (5/8)x = 1/8 => x = 1/5 =>ANSWER.
(9)
Sukumar Natarajan said:
3 years ago
Consider: water is 30 lr and Syrup is 50 lr.
We have to take out 10lr syrup from 50lr. it is clearly 20%.
Note:
It means we are taking out 20 % (= 10 lr) syrup and 20 % (= 6lr) water.
Now we have 40-liter syrup and 24-liter of water remaining. Then we are adding 16-liter water.
Now we have 40-liter syrup and 40-liter water.
We have to take out 10lr syrup from 50lr. it is clearly 20%.
Note:
It means we are taking out 20 % (= 10 lr) syrup and 20 % (= 6lr) water.
Now we have 40-liter syrup and 24-liter of water remaining. Then we are adding 16-liter water.
Now we have 40-liter syrup and 40-liter water.
(17)
Tapan kumar raul said:
1 decade ago
It is a common sense.
Finally in the solution 50% syrup & 50% water will remain.
That means if the solution will (5+3) =8 liters after drawn the mixture syrup will remain 4 liters. That mean the amount of mixture drawn contains 1 liter syrup => 5x = 1 liter.
=> 8x = 8/5 = 1600ml which is 1/5 part of 8 liter.
Finally in the solution 50% syrup & 50% water will remain.
That means if the solution will (5+3) =8 liters after drawn the mixture syrup will remain 4 liters. That mean the amount of mixture drawn contains 1 liter syrup => 5x = 1 liter.
=> 8x = 8/5 = 1600ml which is 1/5 part of 8 liter.
(1)
ADITYA PANDITA said:
7 years ago
@All.
The reason in the last step 8/5 is multiplied with 1/8 (or you could say 8/5 is divided by 8) is because we have found x in liters and the answer is required in parts. The 8 that we have used to divide in the last step is not the total 8 parts but it is the 8 liters we have assumed in the beginning of the answer.
The reason in the last step 8/5 is multiplied with 1/8 (or you could say 8/5 is divided by 8) is because we have found x in liters and the answer is required in parts. The 8 that we have used to divide in the last step is not the total 8 parts but it is the 8 liters we have assumed in the beginning of the answer.
(7)
Kousik Maji said:
1 decade ago
Here total mixture is(3+5)=8.
Now syrup=5/8 and water=3/8.
If we take some mixture and added same amount of water then amount of syrup will be 1/2 and water 1/2.
Now the amount of syrup present in removed mixture is 5/8-1/2=1/8.
Now 5/8 syrup present in mixture 1.
1/8 ........................(8/5)X(1/8)=1/5.
Now syrup=5/8 and water=3/8.
If we take some mixture and added same amount of water then amount of syrup will be 1/2 and water 1/2.
Now the amount of syrup present in removed mixture is 5/8-1/2=1/8.
Now 5/8 syrup present in mixture 1.
1/8 ........................(8/5)X(1/8)=1/5.
Umesh said:
7 years ago
1/5 of 8 is 1.6 ------->remaining=6.4.
We have to remove 1/5 of liquid and add 1/5 of water(1.6 of water).
1/5 of 3=.6 -----> remaining=2.4.
1/5 of 5=1 -----> remaining=4.
6.4 of liquid =2.4 of water + 4 of syrup.
Which means add 1.6 of water to make to make composition equal and 1.6 is 1/5 of 8.
We have to remove 1/5 of liquid and add 1/5 of water(1.6 of water).
1/5 of 3=.6 -----> remaining=2.4.
1/5 of 5=1 -----> remaining=4.
6.4 of liquid =2.4 of water + 4 of syrup.
Which means add 1.6 of water to make to make composition equal and 1.6 is 1/5 of 8.
Shriyash sharma said:
8 years ago
Formula.
Final volume or the ratio of solute A=initial volume or ratio solution A(1-solute to be replaced/total volume)^n.
let A=syrup, B=water.
Putting in formula:
assuming volume is 1litre.
A=5/8, B=3/8.
applying formula on solute A because it will be reduced after an operation.
so,
4/8=5/8(1-x/1),
x=1/5.
Final volume or the ratio of solute A=initial volume or ratio solution A(1-solute to be replaced/total volume)^n.
let A=syrup, B=water.
Putting in formula:
assuming volume is 1litre.
A=5/8, B=3/8.
applying formula on solute A because it will be reduced after an operation.
so,
4/8=5/8(1-x/1),
x=1/5.
Karthik said:
7 years ago
Let take 5 parts of syrup as 50% of the liquid and 3 parts of water as 30% of the liquid. In order to make both the liquids equal, we have to reduce syrup by 10% and raise water by 10%. So, the total quantity of water we have to add or quantity of liquid we have to draw is 20% which is 1/5 of the liquid.
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