Aptitude - Alligation or Mixture - Discussion

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 becomes 4:4, So change in syrup is (5-4) in 5 units so = 1/5.

When a mixture is drawn, both syrup and water is drawn equally.

So, if 1 part from water and 1 part of syrup(total 2 parts) is drawn, the ratio of 3:5 becomes 2:4. When replaced wit 2 parts of water, gives the ratio 4:4 i..e 1:1.

Therefore mixture drawn is 2/8 or 1/4.

Can anyone Explain the formula used in these question?

Very helpful, thanks for helping @Surendrareddy.

Can you explain?

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

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.

@All.

The reason in the last step 8/5 is multiplied with 1/8 (or you could say 8/5 is divided by 8) is because we have found x in liters and the answer is required in parts. The 8 that we have used to divide in the last step is not the total 8 parts but it is the 8 liters we have assumed in the beginning of 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.

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.