Aptitude - Alligation or Mixture - Discussion

How we get 5x+24=40-5x?

A container is filed with 3 part water & 5 parts syrup, so total we have 8 parts or mathematically we can say,

3/8 water.
5/8 syrup.

Suppose we withdraw x parts of mixture then this will contain,

3/8(x) water.
5/8(x) syrup.

Now we have to add same amount of water the amount of water and syrup will be equal, so mathematically.

3/8-3/8(x) +x = 5/8-5/8(x).

It will give x = 1/5.

Why do we add y in this step 3/8[x-y] + y = 5/8[x-y] ?

The rest of the steps are perfectly understood! Thanks :),.

Hey guys I think this is useful formula for this question:

1/2(difference in parts/greater part).

1/2(5-3/5).

1/5.

From where did you get 1/8 in finding the final result?

How we find the % of thing?

There has to be a direct formula for this.

Anyone has it?

Mean litre, m = (l+s)/2.
m = 4.

Proportion x = (l-m)/l.
x = 5-4/5.
x = 1/5.

Pure and Simple.

I cannot understand. Its so difficult for me. Please explain in another way.

Let there be 8 liters of solution, in which 3/8 liter be water and 5/8 lt be syrup. As we can see syrup is more than water so of course some syrup is to be replaced with water. As it is a solution and we can't remove only syrup or water so we have to remove the whole solution and replace it with water.

Now using ratio and proportion (5-(5x/8))/(3-(3x/8)+x) = 1/1.

As some part of syrup will be removed we also have to remove water as i have told that we are replacing some part of whole solution with water thats why we are subtracting 5x/8, 3x/8 from numerator and denominator respectively, now after removing solution we have add equal quantity of water thats why we will add water in denominator which will be equivalent to the quantity of the solution removed i.e 5x/8+3x/8=x. On the RHS side value will be as we want both the syrup and water in same proportion i.e 1/1.