Aptitude - Alligation or Mixture - Discussion

It is a common sense.

Finally in the solution 50% syrup & 50% water will remain.

That means if the solution will (5+3) =8 liters after drawn the mixture syrup will remain 4 liters. That mean the amount of mixture drawn contains 1 liter syrup => 5x = 1 liter.

=> 8x = 8/5 = 1600ml which is 1/5 part of 8 liter.

Let volume is 8.

Water = 3/8 syrup = 5/8.

According to question,

Suppose y mixture(water,syrup)are drawn.

Water quantity is 3y/8 and syrup quantity is 5y/8.

3/8-3y/8+y = 5/8-5y/8.

y = 1/5.

Ratio given is 3:5 (AS 3 Part water & 5 part syrup).

Take even LCM of 3 & 5 i.e. 24, 30 etc.

Suppose we take 24 as LCM.

Now divide LCM by 8 (addition of ratios i.e. 3+5).

So, 24/8=3.

Now, multiply both the terms of ratio by 3.

So we get 9 (water) and 15 (syrup).

As we have to make equal ratio we have to transfer 3 to water from syrup i.e. 15. So that both becomes 12.

So we get 3/15= 1/5.

Can we able to solve this problem in alligation method, if so explain?

How would you taken 1/8 as a part of mixture in the last step? could you please explain?

Let us assume there is total 80 liter of mixture I take 80 for easy division of water and syrup you can take any number or x. So mixture contains 3 part water and 5 part syrup mean there is total 8 part.

8 part is 80.
So 1 part will be 80/8 = 10 litre.

Water is 3 part=30 litre.
Syrup is 5 part=50 litre.

Let why litre of syrup is taken out and replace with water for an equal proportion of water and syrup.

Then the quantity of water = quantity of syrup.

30 + y = 50 - y.
By solving y =10 litre this quantity is taken out form syrup 50 litre.

So this is how many parts of syrup. It is 10/50 = 1/5 part since the answer is in part according to question 1/5th part of syrup should take out and replace by water. You can solve accordingly above with x litre instead of 80litre but x can confuse so always take numerical value for easy calculation. Thanks, I hope it is understandable.

Hi, To make this easier to understand, let us conduct a balance of all the things involved in this problem.

Consider A to be the initial amount of liquid in a vessel which contains 3 parts water and 5 parts syrup.

Let B be the amount of this liquid to be removed and C be the amount of water to be added to get "D" amount of liquid that has 50% water and syrup.

Writing it in the form of an equation, We have A + C = B + D.

From the question, we can see that the amount of liquid = amount of water added.
Hence C = B, A = D.

Now assuming the vessel to contain 1 liter of liquid, by conducting an input/output balance for water, we have:

(3/5 + 3)%A + (100)%C = (3/5 + 3)%B + (50%)D, [100% because it is pure water]

As A is 1 liter and A = D and B = C,

We have (0.375 x 1) + C = 0.375 x C + (0.5 x 1),

C = 0.2 litre or 1/5 liter.

Hope this will helpful for all.

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).

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

The Formula is /2*[Big value -small value/ Big value].