Aptitude - Alligation or Mixture - Discussion

I am getting 8/5 as the amount to be replaced. If there is 8litres of the total liquid then 3 litres is water and 5 litres is syrup. Now suppose if you remove x litres of the liquid the remaining liquid is 8-x.

In this 8-x, 3/8(8-x) is water and 5/8(8-x) is syrup.
Now if we add x litres of water to it the equation we get is
3/8(8-x)+x=5/8(8-x) since both the syrup and the liquid equals 4/8

Solving this equation we get x=8/5

Where did 1/5 come from? Please somebody explain. I am highly confused.

Attention to those who want to understand the solution provided with the question.

Suppose the vessel initially contains 8 litres of liquid. ------> vessel contains => 8l mixture.

Let x litres of this liquid be replaced with water.

Quantity of water in new mixture = 3 - (3x/8) + x litres.

------ >[3lit water it originally contained] - [ (3x/8) l water which was removed when you removed 'x' l mixture] + ['x' litre water that you added].

Hope that'll justify the remaining solution too.

A 10 litre container holds a mixture of water and sugar, the volume of sugar being 15% of total volume. A few litres of the mixture is released and an equal amount of water is added. Then the same amount of the mixture as before is released and replaced with water for a second time. As a result, the sugar content becomes 10% of total volume. What is the approximate quantity of mixture released each time? please solve this sum?

Can anyone solve this?

Given : 3 part is water.
5 part is syrup.

Therefore the total mixture content becomes 8.

We want the half of this complete mixture means half water and half syrup.
So if we add 1 in 3 parts we get 4 i.e. 4/8 = 1/2.
And if we subtract 1 from 5 again we get 4 i.e 4/8= 1/2.
Therefore we get the half-half content of the water and syrup.
In percentage, we added 10% and reduced 10% therefore 10% + 10% = 20%.
And 20% = 20/100.
So, we get 1/5.

Let be x liters of mixture.

From equation quantity of pure liquid = x*(1-y/x)^n.

Where why is quantity of water used.

N is no. of times water replaces the liquid.

x liters of mixture and why liters of water final quantity of pure liquid = 1/2*x.

So from equation 1/2*x = 5/8*x(1-y/x).

Where 5/8*x is the initial quantity of syrup.

We need to find out y/x.

So, 1/2 = 5/8*(1- y/x).

1-(y/x) = 4/5.

y/x = 1-(4/5).

y/x = 1/5.

We know that water is 3 part and syrup is 5 part.
So total amount of mixture must be multiple of 8,
If we take 40 lit mixture.
It must contain 15 lit water and 25 lit syrup.
Now we have to make it 1:1.

i.e-20 lit water and 20 lit syrup.

Now we have to draw 5 lit of syrup from the mix.
When we drew out 8 lit of mix then only it contains 5 lit syrup.
8 lit of water added to the mix makes water and syrup 1:1.
8 out of 40 is 1/5.

Let the volume of the mixture be 8 litres, in which 3 litre is water and 5 litres is syrup.

Now add 2 litre of water in the mixture, the volume becomes 10 litre and the ratio becomes 1:1.

Since the earlier mixture was 8 litre in volume.

Therefore we have to subtract 2 litres from the new mixture, so as it becomes 8 litres.

Now calculate how much part of the mixture was subtracted from the new mixture i.e. (2/10 or 1/5).

For 62.5% water, to get to 50%, 12.5 must go which is exactly 20% of 62.5.

Syrup is to water = 3 : 5.

% water in mixture = 5/8*100 = 62.5%.

Desired % of water = 1/2*100 = 50%.

Difference = 62.5-50 = 12.5%.

To get 50% of water the 12.5% must go.

Hence Formula = Difference/Current Water in Mixture.

= 12.5/62.5 = 1/5 = 20 %.

5 syrup parts of 8 = 62.5% syrup, to get to 50%, 12.5 must go which is exactly 20% of 62.5.

It is simple as Kiran said. Suppose you have total (means 100% solution) is 8 litre. In which you have 5 parts of milk means 60% milk and 3 parts of water means 40% water. Now you have to make mixture 50%-50%. So you have to reduce 10% milk and increase 10% water means if you mix 20% extra water in that then it will reduce quantity of milk 10% and increase water 10% in solution. That's it answer is 20% = 20/100 = 1/5.

Hi.

People who didn't understand why the answer is 1/5 and not 8/5.

It's because of twist in question.

They asked what part of the total mixture.

3 part water + 5 part liquid = 8.

Assume 8 liter is the total mixture.

We got 8/5 liter now see what 8/5 liter percentage in 8 liters.

Ie (8/5) / 8.

= 8/5 * 1/8.

= 1/5.

Trick is in question. So in options they didn't mention units because its a const.

Thank you.