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# Mixture and Alligation #19

 19. In what ratio must water be mixed with milk to gain $16\dfrac{2}{3}\%$ on selling the mixture at cost price? A. 1 : 4 B. 6 : 1 C. 1 : 6 D. 4 : 1

Explanation:

Let CP of 1 litre milk = Rs.1

SP of 1 litre mixture = CP of 1 litre milk = Rs.1

Gain $=16\dfrac{2}{3}\%=\dfrac{50}{3}\%$

CP of 1 litre mixture $=\dfrac{100}{\left(100 + \text{Gain}\% \right)}× \text{SP}$
$=\dfrac{100}{\left(100+\dfrac{50}{3}\right)}× 1=\dfrac{100}{\left(\dfrac{350}{3}\right)}\\=\dfrac{300}{350}=\dfrac{6}{7}$

 By rule of alligation, CP of 1 litre water CP of 1 litre milk 0 1 CP of 1 litre mixture $\dfrac{6}{7}$ $1-\dfrac{6}{7}=\dfrac{1}{7}$ $\dfrac{6}{7}-0=\dfrac{6}{7}$

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

Ajay Sah
2013-06-01 18:53:36
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.

lucky
2015-07-23 19:06:47
still i am not understanding what u did ajay
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Jyothi
2013-06-02 22:09:23
Dear Ajay,

The answer given is right. Let me explain where u went wrong.

C.P. of Mixture is not 5/6

You calculated the gain amount as 50/3% of 1 = 50/300 = 1/6 which is wrong

The 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%
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