Aptitude - Alligation or Mixture - Discussion

3:5 is the ratio given take the largest number in it which is 5.
as per question half of milk and syrup so, 5:5 in large number.
See the difference which is 2 of the taken ratio is 10 so answer is 1/5.

@Victor.

Your answer is helpful to solve this problem. Thanks.

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.

1/5 of 8 is 1.6 ------->remaining=6.4.

We have to remove 1/5 of liquid and add 1/5 of water(1.6 of water).

1/5 of 3=.6 -----> remaining=2.4.
1/5 of 5=1 -----> remaining=4.
6.4 of liquid =2.4 of water + 4 of syrup.

Which means add 1.6 of water to make to make composition equal and 1.6 is 1/5 of 8.

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.

It's simple, but we can't understand what's meaning of question so the meaning of the question is how syrup is removed in the mixture.

So they said half water +half syrup=8.
Then syrup remove is 5-4 =1.
Then in ratio 1/5 parts of syrup is removed that's it.

Let take 5 parts of syrup as 50% of the liquid and 3 parts of water as 30% of the liquid. In order to make both the liquids equal, we have to reduce syrup by 10% and raise water by 10%. So, the total quantity of water we have to add or quantity of liquid we have to draw is 20% which is 1/5 of the liquid.

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.

Total mixture=3+5=8.
Take lcm of 1/3+1/5=8/5.

The hole 8/5 dived by 8 -----> 8/5/8.
8/5*1/8 = 1/5.

Can you explain?

How can we say that mixture drawn off would be 3/8y and 5/8x?