Aptitude - Alligation or Mixture - Discussion

1/2* (bib value-small value) /big value.

Here, big value=5.

Small value = 3.

After putting value in above formula, we get,

1/2* (5-3) /5.

1/2* 2/5.

1/5 = 1:5.

Correct answer for the question asked "how much of the *mixture* must be drawn off" is 8/5 Or 1.6 (which consists of some part or proportion of water and syrup).

> while the c option given is the correct answer of "what is the proportion of syrup in the mixture drawn off"=1/5.
> while proportion of water in the mixture drawn off = 0.6/3 OR 1/5 (i am proving these below).

Proof:

As given in the question that total quantity (qty) of mixture in a vessel is 8 liters <3 parts of water + 5 parts of syrup>.
Now, we can find through it total ratio of water and syrup in the mixture by this way;

3/8*100 = 37.5% water.
5/8*100 = 62.5% syrup.

Let "x" is the quantity of that mixture drawn off.
& "y" is the quantity of water replaced.

As quantity of mixture drawn off is equal to quantity of replaced water, therefore;
=> x = y .........(euq-1).

Now, if we subtract proportion of water(3x/8) in the mixture drawn off from total quantity contain in the vessel (3) and then add quantity of water replaced which is "y" then it will be equal to half quantity of resulting mixture means last mixture.

"
=> 3 - 3x/8 + y = 1/2 * 8.
=> 3 -3x/8 + y = 4.
=> (-3x+8y)/8 = 4-3.
=> (8y-3x)/8 = 1.
=> 8y-3x = 8........ (equ-2).
now I will put value of "y" from equ-1 in equ-2 to solve for value of "x".

=> 8x - 3x = 8.
=> 5x = 8.
=> x = 8/5 ( this is showing that total quantity of mixture drawn off in liters is 8/5 OR 1.6 ).
Now, I will find out ratio or proportion of water and syrup in the mixture drawn off means in this total quantity=1.6.

Proportion of water in the mixture drawn off =3/8 * 1.6 = 0.6 ltrs.
Proportion of syrup in the mixture drawn off = 5/8 * 1.6 = 1 ltrs OR (1.6 - 0.6).

Total quantity of syrup drawn of is 1 out of 5 which in terms of proportion will be write as 1/5.
Quantity of water drawn of is 0.6 out of 3 which in terms of proportion will be = 0.6/3 OR 1/5.
Now, total quantity of syrup after drawn off = 5 - 1 = 4 liters (half of total quantity 8 liters).

Like wise quantity of water after drawn off and replaced with water = 3 - 0.6 + 1.6 = 4 liters (half of total quantity 8 liters).

Given : w:s=3:5,
After removal of x litter the ratio becomes w:s=1:1,

Quantity of water before and after is,
3/8 - 3x/8 +x = 1/2.
5x/8 = 1/8.

x = 1/5 this is the answer and it is a simple method.

5 parts be taken as 50%.
3 parts be taken as 30%.
Equal parts syrup and water be taken,
Then water increased to 20% .
Therefore 20 /100 = 1/5.

Initially W : S=3:5.

After adding water W:S=1:1
Since only water is adding Qty of Syrup will change.
W:S=3:5.
W:S=5:5.
Difference in water =2 part.
Total =(5+5)=10 part.

2/10=1/5 Ans.

Can we assume xth part of the mixture be removed and replaced by water?

Can anyone do it by allegation method?

Thanks @Kiran & @Jitender.

Initially, there were 3/8 water,

We will remove 3x/18 from water and add x water [x is the qty of the liquid which was removed.]
So new water = 3/8 - 3x/8 + x

The same way we can say new syrup 5/8 - 5x/8,
So the equation will be

3/8 - 3x/8 + x = 5/8 - 5x/8,
(3 - 3x + 8x)/8 = (5-5x)/8,
3 + 5x = 5 - 5x,
10x = 2,
x = 1/5;

so 1/5 is the answer.

water : syrup=3:5
requeired 1:1
3:5::a:b=1;1
3b=1
5a=1
a=1/5.