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i want to clear my concept of alligation. a vessel is filled with liquid, 3 parts of which are water and 5 parts are syrup. how much of the mixture must be drawn of and replaced with water so that the mixture may be half water and half syrup?? ti i solved this question. and i got my correct answer 1/5...but i am confused how it works in allegation to get ratio of two elements using one elements in question??

like this image explains basic method to find ratio of two elements i have used this method and got my ratio 5:1 but dont know how????? plz help....thanks

Neeraj Sharma
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1 Answers1

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I am not exactly sure what your question is, but perhaps you are looking for a way to write your solution mathematically?

We can do this very simply. Let the original (and final) total volume be $V.$ It follows that the volume of syrup is $\frac{5}{8}V.$ Now, let $r$ be the fraction of the original volume that is drained. Observe that the amount of syrup left after this operation is $\frac{5}{8}V(1 - r).$ This is equal to $\frac{1}{2}V,$ as given in the problem. Solving, we get $$\frac{5}{8} - \frac{5}{8}r = \frac{1}{2}$$ $$\frac{5}{8}r = \frac{1}{8}$$ $$r = \boxed{\frac{1}{5}}.$$

And we are finished! Hope this helped.

K. Jiang
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