Aptitude - Alligation or Mixture - Discussion

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%.

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%.

The right Answer is 25%.

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.

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.

Let, CP=SP = x
CP of Milk(M) = Mx
SP of Milk & Water(M+W) = (M+W)x,
Now, (M+W)x-Mx = Mx/4,
M:W = 4:1.

@ Pankaj:
The explanation states that the normal cost of milk is actually Re. 1. Now this dishonest milkman is buying some of that milk, adding some water and selling the new mixture for Re. 1 (when the actual value should be lower). So since he is selling the mixture at Re. 1, that becomes his selling price. This is because he has made a profit due to having used some water to dilute it. Now we need to figure out how much of the actual milk has gone into the final product and since water is free, the cost of the milk becomes the cost price.
So:
Cost price of milk + 25% profit = Selling price of milk mixture
Lets assume the cost price of milk is x.
x + 0.25x = 1.00 (since the selling price of mixture is 1 and the profit is 25% of cost price)
1.25x = 1.00
- we all hate decimals, so lets make it easier:
125x = 100
x = 100/125 = 4/5(thats where it comes from). Now that multiplication by 1 is really useless in this problem. Unless the problem, specifically states that he sold something like 10 liters, there is no need multiply by total liters sold. Then do alligation to figure out how much milk and how much water.

Hope that helps.

@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%.