What ratio must water be mixed with milk to gain 16 2 3 by selling the mixture at cost price?

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Answer: Option C

Explanation:

Let CP of 1 litre milk = Rs.1SP of 1 litre mixture = CP of 1 litre milk = Rs.1Gain $=16\dfrac{2}{3}\%=\dfrac{50}{3}\%$CP of 1 litre mixture $=\dfrac{100}{\left(100 + \text{Gain}\% \right)}× \text{SP}$

$=\dfrac{100}{\left(100+\dfrac{50}{3}\right)}× 1=\dfrac{100}{\left(\dfrac{350}{3}\right)}\\=\dfrac{300}{350}=\dfrac{6}{7}$

Quantity of water : Quantity of milk $=\dfrac{1}{7}:\dfrac{6}{7}=1:6$

Let c.p. of milk = re 1, then

s.p. of Mixture =  c.p. of milk = re 1

given gain= 50/3%

gain amount = 50/3% of 1 = 50/300 = 1/6

We know that,

C.P. of Mixture = S.p. of mixture - gain on mixture

                       = 1 -  1/6 = 5/6

Now require ratio = d-m : m-c

                             1-5/6 : 5/6 - 0

                             1/6 : 5/6

                             1:5.

so, I think Your answer is wrong. 

still i am not understanding what u did ajay

Dear Ajay,The answer given is right. Let me explain where u went wrong. C.P. of Mixture is not 5/6You calculated the gain amount as 50/3% of 1 = 50/300 = 1/6 which is wrongThe gain has to be calculated on the CP of the mixture as we are selling the mixture.Hence  you can not consider it as 50/3% of 1 as the 1 is the CP of 1 litre milk, not the CP of 1 litre mixture)

Hence, to get the answer,  you need to find out the CP of the mixture from the SP of the mixture and the gain%

(use Q&A for new questions)

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