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:
203 comments Page 5 of 21.
Raavan said:
5 years ago
Actually here is a simple way of solving.
As there are total 8 parts (3 parts water and 5 parts syrup), the question is that how much quantity of water is added to make both water and syrup half each, frankly speaking, there is no need to remove water as it is to be added again so 1 part of syrup is removed and added as water, so 1 part of 5 parts is 1/5.
That's simple.
As there are total 8 parts (3 parts water and 5 parts syrup), the question is that how much quantity of water is added to make both water and syrup half each, frankly speaking, there is no need to remove water as it is to be added again so 1 part of syrup is removed and added as water, so 1 part of 5 parts is 1/5.
That's simple.
(48)
Shanmukh said:
5 days ago
In the question, they state that the water and the syrup should be in equal quantities. They have already given three parts of water and five parts of syrup. The total is 8 parts.
So, to make them equal, I have to replace one part of syrup with water so that both are balanced. So, out of the given five parts, we have to replace only one part; therefore, the answer is 1/5.
So, to make them equal, I have to replace one part of syrup with water so that both are balanced. So, out of the given five parts, we have to replace only one part; therefore, the answer is 1/5.
Rohit Thakur said:
1 decade ago
1. Let volume of vessel be x.
Now the ratio is 3:5 initially.
(3/8)x water and (5/8)x syrup.
2. Now let y liter of mixture drawn off.
Means now {(3/8)x - (3/8)y} water and {(5/8)x - (5/8)y} syrup in remaining mixture.
3. Now y liters of water mix to make the equal quantity of both water and syrup,
Then, 3/8(x-y)+y = 5/8(x-y),
y = 1/5x.
Now the ratio is 3:5 initially.
(3/8)x water and (5/8)x syrup.
2. Now let y liter of mixture drawn off.
Means now {(3/8)x - (3/8)y} water and {(5/8)x - (5/8)y} syrup in remaining mixture.
3. Now y liters of water mix to make the equal quantity of both water and syrup,
Then, 3/8(x-y)+y = 5/8(x-y),
y = 1/5x.
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:
9 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:
2 years 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.
(17)
Sukumar Natarajan said:
5 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:
8 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.
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers