Aptitude - Alligation or Mixture - Discussion

NOTE: Liquid = Mixed substance (water, syrup).

Let the volume of the vessel = x litres.
Out of this x liters 3/8 (x) is water & 5/8 (x) is syrup.
Let y litres of liquid is taken out. So out of this, y litres 3/8 (y) is water and 5/8 (y) is syrup.

The water in the remaining liquid is 3/8 (x-y).

The syrup in the remaining liquid is 5/8 (x-y).

Now, y litres of water is added to the remaining liquid so that the final liquid contains half water and half syrup.

=> 3/8 (x-y) +y=5/8 (x-y).
=>y=1/5 (x).
Or y = 1/5 (x).

Answer: The amount of liquid drawn out = The amount of water added = 1/5 of x.

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.

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.

I think the issue with some of the guys here is they find these mathematical theories hard to understand. Let me make it simpler for them.

They didn't give the volume of vessel in the question so never mind that. The vessel contains 8 parts of liquids (i.e. - 3 parts of water and 5 parts of syrup).

What they are asking is to make the mixture into half water and half syrup i.e. - 4 parts of water and 4 parts of syrup. To make it happen you need to take 1 part of syrup out of the vessel (which is 1/5th of the total syrup) and add 1 part of water instead and thus you get the answer 1/5!

NOTE: Liquid = Mixed substance (water,syrup)
Let the volume of the vessel = x liters.
Out of this x liters 3/8(x) is water & 5/8(x) is syrup.
Let y liters of liquid is taken out. So out of this y liters 3/8(y) is water and 5/8(y) is syrup.
The water in the remaining liquid is 3/8(x-y) .
The syrup in the remaining liquid is 5/8(x-y).
Now y liters of water is added to the remaining liquid so that the final liquid contains half water and half syrup.
=> 3/8(x-y)+y=5/8(x-y)
=>y=1/5(x)
or y = 1/5(x).
Answer: The amount of liquid drawn out = The amount of water added = 1/5 of x.

Let us consider the mixture to be of 8 litres (3 Litres of water + 5 litres of Syrup).
Amount of Water in the 8 litre Mixture : 3/8.
Amount of Syrup in the 8 litre Mixture : 5/8.
For easy calculation, I am considering the mixture to be of 10 litres.
Hence Amount of Water in the 10 litre Mixture : 3/8 * 10 = 3.75.
Amount of Syrup in the 10 litre Mixture : 5/8 * 10 = 6.25.


We need to replace 1.25 litres of syrup from the mixture and replace with water 50 make it 5 / 5. Hence we need to replace 2 litres of mixture (.625+.375) * 2.

2 Litres out of 10 litres is 20% or 1/5.

According to me, the solution is;

Water : syrup
30. :50

Total =80 then if x ltr mixture we tack out then the remaining ratio will be 1:1 .So
Take option 1/4 then try 1/4of 80 =20, or we can say 20/80*100= 25% of every (water and syrup).

But here we get vale in fraction, 25%of 30 = 7.5 ., 25%of 50= 12.5,
so this value.
30 - 7.5 =. 22.5
50 - 12.5 = 37.5 + 20 = 57.5.

This value not in ratio 1:1.

So, here ve take vale 1/5 or we can say 20 %of every part. 30*1/5=6
50 * 1/5 = 10.
Thus.
50 - 10 = 40.
30 + 10 = 40 this is in Ratio 1:1.

Let us say that the quantity in the vessel is 8x units. It has 3x water and 5x syrup.
Now, let's say we withdraw 8y units of the mixture are replace them with water. When we take out 8y units of the mixture, we are actually taking out 3y water and 5y syrup. We are adding pure water back into the vessel.

New quantity of syrup = 5x - 5y.
New quantity of water = 3x - 3y + 8y = 3x + 5y.
They are equal to each other.
=> 5x - 5y = 3x + 5y.
=> 2x = 10y,
=> y/x = 2/10 = 1/5,
=> 8y/8x = 1/5k.

So, 1/5th of the mixture should be taken out and replaced with water.

Let's say after removing some part of the mixture.

The ratio of the remaining mixture is the same i.e. 3:5 for water to syrup.
Now consider this mixture is 8L in total (3+5).
Now once we add 2L of water in the mixture the ratio becomes 5:5 which was desired.
5+5 =10.

So we can say that even in the original mixture the quantity was 10L as 2L was removed from that.
(2L mixture removed and 2L water added).
This satisfies the condition.
Now,
The question is how much of the mixture is to be removed and replaced.
2L/10L i.e.1/5.
1/5 will be the answer.

Initially we have 3 :5 ratio of w:s.

We are replacing only water so syrup quantity will remain same.
we want mixture in half that is mixture ratio
of w: s will be 1:1
but we know syrup quantity won't change so multiply mixture ratio in order to get same quantity of syrup as before i.e. 5
so multiply mixture ratio by 5
we get final ratio of water to syrup (w:s)=5:5.

So,
initially 3:5
finally 5:5
from above we can say that 2 part of water changing
and no of a part in the final mixture is 5+5=10 part.
So,
2/10 =1/5.