Aptitude - Alligation or Mixture - Discussion

You guys all great. Knowing how to solve a problem in an easy way is great and explaining to others is a bigger than that. Great helping kind. Once again Thank you all.

Please, anyone solve it in alligation formula.

New quantity of syrup = 5x - 5y.
New quantity of water = 3x - 3y + 8y = 3x + 5y.
They are equal to each other.
=> 5x - 5y = 3x + 5y.
=> 2x = 10y.
=> y/x = 2/10 = 1/5.
=> 8y/8x = 1/5.

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.

Superb @Kiran.

How came 5x + 24 = 40 - 5x?

Hi.

People who didn't understand why the answer is 1/5 and not 8/5.

It's because of twist in question.

They asked what part of the total mixture.

3 part water + 5 part liquid = 8.

Assume 8 liter is the total mixture.

We got 8/5 liter now see what 8/5 liter percentage in 8 liters.

Ie (8/5) / 8.

= 8/5 * 1/8.

= 1/5.

Trick is in question. So in options they didn't mention units because its a const.

Thank you.

8/5 * 1/8 is done because part of the mixture has to be replaced.

Since a part of the mixture is 1/8, the final answer is multiplied with it.

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.

Attention to those who want to understand the solution provided with the question.

Suppose the vessel initially contains 8 litres of liquid. ------> vessel contains => 8l mixture.

Let x litres of this liquid be replaced with water.

Quantity of water in new mixture = 3 - (3x/8) + x litres.

------ >[3lit water it originally contained] - [ (3x/8) l water which was removed when you removed 'x' l mixture] + ['x' litre water that you added].

Hope that'll justify the remaining solution too.