Aptitude - Alligation or Mixture - Discussion

From where 100/125 is come ?

plz tell soon

@ 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.

@ Pankaj:
Its a formula for finding the C.P when the gain % is given.C.P=((100/(100+gain%))+selling price)

@amir:

"milk:water==100:x"
where x is gain%

Soln:
m:w==100:25==4:1
that means water percentage is=
1/5*100=20%
answer==20

Then how we take 1/5 if we do 4/1= its become 4/5(4.. second become by 4+1=5) whay u take 1/5 plz explain me

Explain whole Question once again.

What is rule of alligation?

let assume milk to be 100..
After mixing water he gets profit of 25 i.e. he sell mixture (water+milk) at 125..

now percentage of water in full mixture is 25/125*100= 20%

I saw the important formula section but I'm still unable to understand the use of rule of allegation.

In every problem I come across I find it used in a diff manner.

Can someone explain it?

CP of 1 liter of milk = Re1.
SP of 1 liter of milk = Re1(given).

Gain = 25%(for the mixture [M+W]).

CP of milk(mixture) = (SP*(100/100+gain)) = 1*100/125 = 4/5.

Hence by allegation rule,

Milk(old) water
CP = Re1(dearer) CP = 0(for milk)(cheaper)
Mixture
CP = 4/5(mean).

Cheaper:Dearer = (1-4/5)/(4/5-0) = 1:4.
Water : milk = 1:4.
Water% = 1/5*100 = 20%.