Aptitude - Alligation or Mixture - Discussion

Suppose initial quantity of mixture is 1 lit.
ratio water:syrup = 3:5,so syrup is 3/8
alligation method

3/8 1(pure water so taken as 1)

1/2

1/2 1/8

qt of mixture 1/2
-------------= ---
qt of water 1/8

1-x/x=4,so x=1/5 (x= quatity of water removed or qt. of syrup
withdraw)

Formula for this type of question:.

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

Here x=8/5 is the amount in liters that has been added to make up 8 liters in total. This added quantity constitutes some part of the total volume. Right? So, this some part is stated as (x/8). Hope everyone's doubt on this has been cleared. => (8/ (5*8) ) =1/5.

1/5th is the part (not liters) from the total 8liters that has been added. Thank You.

Good victor.

I did not get it why 8/5 is multiplied with 1/8.

Great surendra reddy.

The first one itself is short solution.
as we assume total soln as 8litre
so if x litre of water is added by replacing
So net water remains is 3-3x/8+x in 8 litre
and syrup is 5-5x/8
equalize both as both becomes equal in content aftr previous replacement.

we get x=8/5
but this is replecement if we assume cotent of vessel =8l
so part of replcement=replced amount/total amount
this means (8/5)/8 = 1/5 ans

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.

Thanks ameer.

I think amir done good solution.