Problem:

Let there are two cone.one contains 1 litre milk and other contain 1 litre water.if i take one cup milk from first and droped into second.then again i took one cup mixture from seecond and droped into first one.Is the amount of milk in first is same as amount of water in second?

Ans: yes

explanation:

let amount of liquid in cup is c.

cane 1 cane 2

step 1:

Water 0 1

milk 1 0

step2:

water 0 1

milk 1-c c

conc^n of milk in second cone is c/(1+c) and of water 1/(1+c)

in one cup amount of milk =c* c/(1+c) amount of water c/(1+c)

step3:

water c/(1+c) 1-c/(1+c)=1/(1+c)

milk 1-c+c*c/(1+c)=1/(1+c) c-c*c/(1+c)=c/(1+c)

...proved

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