In what ratio the water must be mixed with the milk to gain 10% profit on selling the mixture?

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Discussion :: Alligation or Mixture - General Questions (Q.No.10)

10.

In what ratio must water be mixed with milk to gain 16

% on selling the mixture at cost price?

[A].	1 : 6
[B].	6 : 1
[C].	2 : 3
[D].	4 : 3

Answer: Option A

Explanation:

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

S.P. of 1 litre of mixture = Re.1, Gain =	50	%.
3

C.P. of 1 litre of mixture =		100 x	3	x 1		=	6
350	7

By the rule of alligation, we have:

C.P. of 1 litre of water C.P. of 1 litre of milk
0	Mean Price	Re. 1

Ratio of water and milk =	1	:	6	= 1 : 6.
7	7

Moncy said: (Oct 31, 2010)
Can anyone please explain me how they took gain=50/3 as 350/3 while computing c.p of 1lt mixture..Please explain it for me...

Jose said: (Nov 8, 2010)
I can't understand 3/350.

Pratik said: (Nov 27, 2010)
It is the gain % so 100+ 50/3 = 350/3 and putting this into the formula we get 100/350/3 = 100*3/350

Raghaav said: (Dec 19, 2010)
can any one explain this sum please

Habib said: (Feb 25, 2011)
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

Mini said: (Sep 21, 2011)
Can you please tell me how we get 1/7 under 1 litre of water?

Dilip said: (Sep 24, 2011)
Here the gain% is 16.66 i.e in 100 lit milk, 16.66 lit water is required to be added. Hence ratio becomes, 16.66/100 = 1/6.

Ashu said: (Apr 21, 2012)
How we know that C.P of water will be on left side and of milk on right side? how does it affects if we change them?

Maggi15 said: (Mar 5, 2013)
Agree with Dilip. The new ratio of 2 elements will be same as the profit/100. Say profit is 25% then the ratio will be 25/100 = 1/4. Hence, in 1000 litres of mixture, 200 litres of water + 800 litres of milk.

Harsh said: (Mar 27, 2013)
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.

Girish said: (Sep 27, 2013)
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.

Yuvraj said: (Feb 20, 2014)
Please could explane me how is come 50/3 ?

Pooja said: (Jun 16, 2014)
Can anyone say why we are taking as 3/350?

Manan said: (Jul 18, 2014)
@Yuvraj : (16*3+2)/3 = (48+2)/3 = 50/3. Thats how a mixed fraction is solved.

Sowmya said: (Apr 6, 2015)
Blindly assumed like this type problems. 16 2/35% = 50/3%. So, 50/3/100 = 50/3*1/100 = 50/300 = 1/6. So, 1:6.

Alagu said: (Apr 23, 2015)
How the C.P of 1 liter milk is Re. 1?

Oken said: (May 9, 2015)
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.

Floretamit said: (Jun 28, 2015)

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.

Shivani said: (Jul 13, 2015)
How we get to know either they are asking milk to water ratio or water to milk ratio that's why it can be 6:1 and 1:6?

Supritha K.S. said: (Jul 26, 2015)
Why is C.P. of 1 liter of milk taken on the left hand side as per the rule of alligation in this problem. Unlike C.P. of 1 liter of milk which is taken on the right hand side in 6th sum and other sums?

Amit said: (Jul 31, 2015)
Yes @Supritha you are right. How can we take lower C.P water at right side in problem no. 6?

Ana said: (Aug 5, 2015)
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.

Rahul said: (Sep 18, 2015)
How it is equal to fraction value?

ABHISHEK PRABHAKAR said: (Jan 2, 2016)
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.

Pratap said: (May 26, 2016)
How is it 3/350 on calculating C.P? Please explain.

Pidu said: (Jul 28, 2016)
They have used C.P. formula. C.P = (100/(100 + gain%) * S.P). So, (100/(100 + (50/3)) * 1). 100 * (3/350) * 1.

Rajeshdharamdasani said: (Aug 31, 2016)
Whey they have assumed C.P of water is 0?

Tiger Karim said: (Oct 26, 2016)
According to question, Millk = 100 , Water = 50/3, Ratio = 50/3 : 100 = 1 : 6.

SUMIT VERMA said: (Oct 31, 2016)
Let the cost price be Rs.100. Since gain is Rs. 50/3. So S.P is 100 + 50/3 = Rs.350/3. Hence, Ratio = S.P - C.P/C.P, (350/3 - 100)/100 = 1/6.

Akshay said: (Nov 26, 2016)
Simple method. % always denote to 100. So, 50/3 : 100 = 1/6.

Princy said: (Jan 11, 2017)
How the selling price of one-litre mixture is 1 re?

Pritam said: (Apr 8, 2017)
I can't understand how 3/350 is coming? Can anybody help me? please.

Thakursaab said: (Apr 16, 2017)

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.

Vishal said: (Jun 11, 2017)
Here, c.p = ((100/(100+gain%))s.p), Here 100 + gain% = >100 + 50/3 = 350/3, 100(3/350) * 1=300/350 = 6/7.

Sowmiya said: (Jun 27, 2017)
How we get to know either they are asking milk to water ratio or water to milk ratio that's why it can be 6:1 and 1:6?

Milad said: (Jul 2, 2017)
according to question. The gaining % is 50/3. so, the percent of water be 50/3. And percent of milk 100. so, W:m =1:6.

Paras said: (Jul 22, 2017)
I too agree that it should be 5/6 instead of 6/7. Same thing was done in 6th question where same logic was applied. It gives ratio 1:5. Please, anyone explain.

Rohit Chaudhary said: (Feb 15, 2018)
In what proportion must water be mixed with spirit to gain 9.09% by selling it at cost price. The quantity of water in the mixture of 1 litter is? Can anyone help me to solve this question?

Cosul said: (May 29, 2018)

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.

Veeranki said: (Jul 9, 2018)
1/6=16 * 2/3%. So take cost price is 100%. and 1 : 1/6 = 6:1.

Pari said: (Aug 1, 2018)
CP+Profit=SP. Profit gave =1/6. SP of 1-litre mixture assumed to be Re1 and CP of 1-litre milk assumed to be Re1 CP+1/6 of CP = SP(which is assumed as 1). So, CP comes out as 6/7.

Sayantan Das said: (Sep 10, 2018)
It will be 6:1 not 1:6.

RIni said: (Sep 25, 2018)
The amount of water =x litre. Amount of milk= 100-x litre. Profit= (x/(100-x))*100=50/3. x=100/7=amount of water. Amount of milk= 100-100/7=600/7. The ratio of the amount of water to milk=1:6.

Ramesh said: (Nov 2, 2018)
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.

Sathish said: (Dec 20, 2018)
Can anyone explain why taking water : milk and not milk : water?

Nitish Raja said: (Apr 5, 2019)
Let cp of milk in% be = 100%, So, milk : water = 100% : 16 2/3%, 100% : 50/3 = 1: 6.

Nadim Miah said: (May 27, 2019)
If 100 is cost price and sp then why do we add 50/3 with cp? Please explain.

P K said: (Sep 24, 2020)
Water always be the same amount, i.e, 100. So the extra gain= mixed water, i.e, 50/3%. water : milk = 50/3 : 100 = 50 : 300 = 1 : 6.