Aptitude - Alligation or Mixture - Discussion

Let total quantity was x and cost price of milk was 100.

Since we have to sell milk with same price but have to gain profit 50/3% of 100 rupee so here selling price will be 100 and cost price of mixture.

== Selling price - Profit.

==100-50/3 = 250/3.

Now, use allegation by x liter milk o milk that is water.

100.
250/3.

250 : 50.
= 5 : 1.

Now the quantity of water that should mixed with milk will be.

1/6*x that is water must be mixed 1/6th weight of milk weight. That means if initial milk was kg kg than 1 liter water must be mixed to get 50/3 % profit by selling on original cost price.

Let you are selling pure milk in 1 rs for each litre.

Now, someday you think to gain more money for this you take some milk out and replace it with water.
say ratio remains of milk to water =1 : x.

Now, you know that water is free hence it cost nothing and still you are able to sell the total 1 litre mixture in same price i.e,1 rs.

Hence
SP=1.
CP = portion of milk present in mixture=1/1+x.
Because you have to just pay for milk in case you purchase it.
Now use gain % formula: sp - cp/cp = (%gain/100).

You will get the answer by solving the equation.

I can give a short cut and very simple method.

Cost of water is taken to b zero if it had some cost then the person would not have mixed the water so cost of water is zero.

So in such question where cost of one ingredient is zero and selling price =cost price the ratio is simply equal to the fractional value of gain%. You can check it on your own.

Let 100 liter milk cost Rs. 100 (it means one liter milk cost Rs. 1).

Since profit should be 50/3 percent, therefore total mixture should be (100+50/3) liter. So that it can give a profit of 50/3 percent. Hence we have to mix 50/3 liter of water in milk.

Therefore the ratio of water to milk in the mixture is (50/3) /100 = 1/6 answer.

As the gain is given in percentage, let us assume for 100 ltrs of milk.

The amount of water mixed is the amount of profit we get.

Amount of water is 16 2/3 i:e 50/3.

Amount of milk is 100.

Therefore required ratio = Qty of Water/Qty of Milk.

= 50/3 /100 =1/6 is the answer.

Let C.P. of 1 litre of milk be Re 1.

Then S.P. of the mixture is also Re 1.

C.P. of 1 titre of the mixture = 1-50/300 = 250/300 = 5/6.

As per my opinion C.P. of 1 litre of the mixture is Rs. 5/6 but everyone told me it should be 6/7.

How is it so? Anybody please help.

Let, 100 litres cost 100 rs.
Now, 100 + y litres cost 350/3 rs.
So re-arranging equations

100 --> 100.
100+y ---> 350/3.

Solving for y we get 16.33 litres.
So that means we add 16 litres more to 100 lit of milk.

So, the ratio is 16 /100 = 0.16.

SP/CP = ( Gain% + 100 )/100,

So u get, SP/Cp=350/300..................(Put gain%=50/3,in form)

Nw u get, CP=(6/7)SP............This gives you the mean price

And hence substitute in alligation formulae....to get the ratio

Let the cost price be Rs.100.

To gain 50/3 milk in mixture=100-50/3=250/3.

Ratio in which milk is present = (250/3 )/100 = 250/300.

Since, mixture is 1.

Ratio in which water is present = 1 - 250/300 = 50/300= 1/6.

CP of milk = X.

Water is added
SP of mixture= 1.1667X.
1.1667X=X+0.1667X.

X=milk 0.1667X=Water.
0.1667/1.1667=0.142.
14.2% = Water and 85.7 % milk.
14.2/85.7=1/6.
The water and milk are in the ratio of 1:6.