3 L water is taken out from vessel full of water and substituted by pure milk. This process is repeated two more times. Finally, the ratio of milk and water in the solution becomes 1728 : 27. Find the volume of the original solution.
A. 3 L
B. 5 L
C. 4 L
D. 9 L
Answer: Option C
Solution(By Examveda Team)
We use formula for it where n = number of time process of out going repeated. y = Out going milk in process. x = Volume of original solution. F = Final milk left in mixture. $$F = x{\left( {1 - \frac{y}{x}} \right)^n}$$ Final quantity of water, $$F = x{\left( {1 - \frac{3}{x}} \right)^3}$$$$\frac{F}{x} = {\left( {\frac{{x - 3}}{x}} \right)^3}$$
$$\frac{{27}}{{1728}} = {\left( {\frac{{x - 3}}{x}} \right)^3}$$
$${\left( {\frac{3}{{12}}} \right)^3} = {\left( {\frac{{x - 3}}{x}} \right)^3}$$
$$\frac{3}{{12}} = \frac{{x - 3}}{x}$$
$$x = 4 \,\text{L}$$
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Comments ( 8 )
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The given ratio may be wrong.
How did u inverse the ratio?
I think, there is problem in the question.
The 2nd part of the question should be "Finally the ratio of milk and water becomes 1721:27."
I think,x= 1728+27=1755.
And why don't u reply comment?
How can F/x be replaced by 27/1728? "x" is the volume of original volume which contains water only. But here 1728 is the amount of milk.
Sir, actually que thoda wrong hai...ratio of volume of solution to final water volume become 1728/27...then only you get 4l as original water volume (or the final solution volume)
This is incorrect. Volume of milk in solution is x -x(1-3/x)^3 and so equation should be x(1-3/x)^3/x-x(1-3/x)^3 = 27/1728
sir solution understand nhi ho raha
so explain it
n if any short trick to solve this type of question