Aptitude - Alligation or Mixture - Discussion

@All.

Here is the shortest method.
Profit is 25%= 1/4.
So, the ratio of water and milk is 1:4.
So % of water 1/5 = 20%.

Let the amount of pure milk in the mixture be x litres.
Since the mixture is sold at the cost price of 1 litre, but he gains 25%, the amount of milk he is effectively selling is:
𝑥=1/1.25 = 0.8 liters of milk
This means that in 1 litre of the mixture, there are 0.8 litres of milk.

Since the total volume of the mixture is 1 litre, the amount of water in the mixture is:
1 − 0.8 = 0.2 liters of water.
Now, the percentage of water in the mixture is:
0.2/1 × 100 = 20%.

The right Answer is 25%.

@Vikas Rawat.

Thank you you explained very well.

How do they determine 4/5 is the mean price of milk and water? We have found 4/5 as the cost price of the mixture. Then how it become the mean price?

Please explain.

Milk. +. Water. = Total mixture.

100% + 25%. = 125%.

25%/ 125% = 1/5 = 20%.

Assume he sells 100 litres of milk.

In those 100 litres, he mixes 25 %of water that means he mix 25 litres of water to 100 litres of Milk.
So , the total mixture is 125 litres.

The profit gained by the seller is nothing but the amount of water added to milk. i.e 25 litres

Now,profit% = amount of water added/total amount of solution * 100.
25/125 * 100 = 20%.

@Rahul.

Excellent explanation. Thanks.

Initially, there is 100% of milk.
After he mixed 25% of water.
Now the mixture becomes 125%.

He asked what is the % of the water in the mixture.
25% in 125% is 20%.
So the answer is 20%.

There's a formula for this in Profit and Loss:

Gain% = Error/(True Value - Error).

Since Gain% = 25% (or 1/4), simply take any True Value and you'll find the Error amount for that.

Now that Error is how much of the True Value (in %), is your answer.

Normally we take True Value as 100 for a direct answer but you can take any value and then find the answer.

Eg. In this case,

1/4 = Error / (100-Error) => Error = 100/5 => 20%.

That's it.