Aptitude - Alligation or Mixture - Discussion

Answer: 1/5th of the vessel volume. Let's assume the capacity of vessel be (3+5=) 8 litres.

Now, the basic principle of all such questions is that when you remove any amount of the mixture, it removes both the liquids in the same ratio as the mixture itself. So, let's suppose we take x litresout of the vessel. This means 5x/8 amount of syrup and 3x/8 amount of water gets removed. which means the remaining mixture has (3-(3x/8)) litres of water & (5-(5x/8)) syrup. Now when we add x litres of water to this mixture, the amount of water and syrup becomes equal. Thus, (x+3-(3x/8)) = (5-(5x/8)) => x=1.6 ltrs.

Since we assumed that vessel is 8 ltrs. in volume=> 1.6/8 = 1/5th of the mixture in the vessel needs to be replaced with water. Hope it helps.

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.

Well said @Surender.

Good explaintion I am not getting this but you solve very well & I get it now.

Simple solution for this;

Given: Vessel contains...water -- 3 parts. Syrup -- 5 parts.

Required: Both should be half-- half

Sol: take one part of syrup and add it to water i.e then both will have 4 parts.

So divide syrup into 5 parts.then one part is 1/5, that is the solution.

Assume 30L water.
50L syrup.
Remove 20L liquid.

Than water will be 20L and syrup is 40L.
Add this 20L to water than 40L and 40L.
20/100 = 1/5.

3 : 5 is given.
1:1 we need,
3 : 5
1*5 : 1* 5
Difference 3 to 5 = 2
Total now 5+ 5
Then 2/ 10 ans is 1/5.

To make the given 3:5 equal we can take out 1 from 5 and add to 3(4:4). Since 1 is taken out from syrup so, the answer will be 1/5.

The ratio of syrup and water is 3:5 after replacing it will half-half(equal) -> 1:1
Because we are adding only water so the ratio of syrup will be same then ratio 1:1 become
5:5 means 2 ratio water is adding, total ratio is 5 + 5=10.
So 2/10=1/5

@Kiran.

Nice explanation.

As there are 3 parts of water and 5 parts of syrup.
total upto 8 parts.In terms of percentage,syrup is 60% and water is 40%.So syrup content to be reduced to 10% and water content to be increased to 10%,total constitutes to 10%+10%=20%.
finally 20%=20/100=1/5