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 4 of 20.
Manisha said:
9 years ago
Let's consider total mix is100 litre, Water = 3parts = 37.5liter.
Syrup = 5parts = 62.5 litre.
We have to draw liquid so that syrup remains.
50 litre for that we have to draw out the quantity of mixture which contains 12.5 litres of syrup.
Now mixture containing 12.5-litre syrup contain = 12.5 * 8/5 = 20 litre.
We have to draw out 20litre mix.
i.e 20/100 = 1/5 mix have to replace for getting 1:1 mixture.
Syrup = 5parts = 62.5 litre.
We have to draw liquid so that syrup remains.
50 litre for that we have to draw out the quantity of mixture which contains 12.5 litres of syrup.
Now mixture containing 12.5-litre syrup contain = 12.5 * 8/5 = 20 litre.
We have to draw out 20litre mix.
i.e 20/100 = 1/5 mix have to replace for getting 1:1 mixture.
Naveen Gaddam said:
7 years ago
In Mixture: 3 parts = water and 5 parts=Syrup.
Given: 5 parts of Syrup(S) ====> 3 parts of Water(W).
So,
for 5 parts of Syrup --> 3 parts Water.
How much for 1 part Syrup --> water=?
1 part syrup= 3/5=0.6 water.
We need to remove 1 part water and 0.6 part syrup and replace with water to equal the mixture= 4S+4W.
The removal mixture of 1.6 parts which is 20% of 8 parts = 20% = 20/100 = 1/5.
Given: 5 parts of Syrup(S) ====> 3 parts of Water(W).
So,
for 5 parts of Syrup --> 3 parts Water.
How much for 1 part Syrup --> water=?
1 part syrup= 3/5=0.6 water.
We need to remove 1 part water and 0.6 part syrup and replace with water to equal the mixture= 4S+4W.
The removal mixture of 1.6 parts which is 20% of 8 parts = 20% = 20/100 = 1/5.
Yogi said:
1 decade ago
The first one itself is short solution.
as we assume total soln as 8litre
so if x litre of water is added by replacing
So net water remains is 3-3x/8+x in 8 litre
and syrup is 5-5x/8
equalize both as both becomes equal in content aftr previous replacement.
we get x=8/5
but this is replecement if we assume cotent of vessel =8l
so part of replcement=replced amount/total amount
this means (8/5)/8 = 1/5 ans
as we assume total soln as 8litre
so if x litre of water is added by replacing
So net water remains is 3-3x/8+x in 8 litre
and syrup is 5-5x/8
equalize both as both becomes equal in content aftr previous replacement.
we get x=8/5
but this is replecement if we assume cotent of vessel =8l
so part of replcement=replced amount/total amount
this means (8/5)/8 = 1/5 ans
Abhidhamm said:
1 decade ago
Ratio given is 3:5 (AS 3 Part water & 5 part syrup).
Take even LCM of 3 & 5 i.e. 24, 30 etc.
Suppose we take 24 as LCM.
Now divide LCM by 8 (addition of ratios i.e. 3+5).
So, 24/8=3.
Now, multiply both the terms of ratio by 3.
So we get 9 (water) and 15 (syrup).
As we have to make equal ratio we have to transfer 3 to water from syrup i.e. 15. So that both becomes 12.
So we get 3/15= 1/5.
Take even LCM of 3 & 5 i.e. 24, 30 etc.
Suppose we take 24 as LCM.
Now divide LCM by 8 (addition of ratios i.e. 3+5).
So, 24/8=3.
Now, multiply both the terms of ratio by 3.
So we get 9 (water) and 15 (syrup).
As we have to make equal ratio we have to transfer 3 to water from syrup i.e. 15. So that both becomes 12.
So we get 3/15= 1/5.
(1)
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%.
G.MUNIYANDI said:
9 years ago
Let water be 0.6 L whereas syrup is 1L.
0.6 + 0.2 = 0.8 : 1 - 0.2 = 0.8
1 : 1,
0.2/1=1/5.
(Here, to solve the problem without complex one thing is to have it in our mind that is what amount of water is taken from a mixture which is filled with the same amount of water again. Thus how much amount of syrup is drawn off from the mixture that is taken in our consideration then 0.2/1 = 1/5 is answer.
0.6 + 0.2 = 0.8 : 1 - 0.2 = 0.8
1 : 1,
0.2/1=1/5.
(Here, to solve the problem without complex one thing is to have it in our mind that is what amount of water is taken from a mixture which is filled with the same amount of water again. Thus how much amount of syrup is drawn off from the mixture that is taken in our consideration then 0.2/1 = 1/5 is answer.
K.S PAL said:
1 decade ago
A container is filed with 3 part water & 5 parts syrup, so total we have 8 parts or mathematically we can say,
3/8 water.
5/8 syrup.
Suppose we withdraw x parts of mixture then this will contain,
3/8(x) water.
5/8(x) syrup.
Now we have to add same amount of water the amount of water and syrup will be equal, so mathematically.
3/8-3/8(x) +x = 5/8-5/8(x).
It will give x = 1/5.
3/8 water.
5/8 syrup.
Suppose we withdraw x parts of mixture then this will contain,
3/8(x) water.
5/8(x) syrup.
Now we have to add same amount of water the amount of water and syrup will be equal, so mathematically.
3/8-3/8(x) +x = 5/8-5/8(x).
It will give x = 1/5.
Ami said:
1 decade ago
Suppose initial quantity of mixture is 1 lit.
ratio water:syrup = 3:5,so syrup is 3/8
alligation method
3/8 1(pure water so taken as 1)
1/2
1/2 1/8
qt of mixture 1/2
-------------= ---
qt of water 1/8
1-x/x=4,so x=1/5 (x= quatity of water removed or qt. of syrup
withdraw)
ratio water:syrup = 3:5,so syrup is 3/8
alligation method
3/8 1(pure water so taken as 1)
1/2
1/2 1/8
qt of mixture 1/2
-------------= ---
qt of water 1/8
1-x/x=4,so x=1/5 (x= quatity of water removed or qt. of syrup
withdraw)
Raavan said:
4 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.
(46)
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.
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