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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,
$$F = x{\left( {1 - \frac{3}{x}} \right)^3}$$
$$\frac{F}{x} = {\left( {\frac{{x - 3}}{x}} \right)^3}$$
$$\frac{{27}}{{1728}} = {\left( {\frac{{x - 3}}{x}} \right)^3}$$
$${\left( {\frac{3}{{12}}} \right)^3} = {\left( {\frac{{x - 3}}{x}} \right)^3}$$
$$\frac{3}{{12}} = \frac{{x - 3}}{x}$$
$$x = 4 \,\text{L}$$

This Question Belongs to Arithmetic Ability >> Alligation

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Comments ( 8 )

  1. Manik Paul
    Manik Paul :
    4 years ago

    The given ratio may be wrong.

  2. Dharshn S
    Dharshn S :
    4 years ago

    How did u inverse the ratio?

  3. Sharmi Sen
    Sharmi Sen :
    4 years ago

    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."

  4. TARIKUL ISLAM
    TARIKUL ISLAM :
    5 years ago

    I think,x= 1728+27=1755.
    And why don't u reply comment?

  5. Ripon Chowdhury
    Ripon Chowdhury :
    5 years ago

    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.

  6. Ishraq Zeya
    Ishraq Zeya :
    5 years ago

    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)

  7. Aamir Naqvi
    Aamir Naqvi :
    5 years ago

    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

  8. Arunmalhotra
    Arunmalhotra :
    8 years ago

    sir solution understand nhi ho raha
    so explain it
    n if any short trick to solve this type of question

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