Question

A mixture comprises water and liquids A and B. The volume of water is 1/3rd of the total mixture and the volume of liquids A and B are in the ratio 5:3. To remove the water, the mixture is passed through a porous medium which completely absorbs the water and partially absorbs liquid A. Altogether this porous medium absorbs 200 ml of the initial mixture. If the ratio of volume of liquids A and B in the residual concentrated mixture becomes 7:9 then find the volume of water absorbed by the porous

Accepted Answer

E. Let total mixture = $24x$. Water = $8x$, Liquid A = $10x$, Liquid B = $6x$. Medium absorbs all water ($8x$) and some amount $y$ of A. Total absorbed = $8x + y = 200 \implies y = 200 - 8x$. Residual A = $10x - y = 10x - (200 - 8x) = 18x - 200$. Residual B = $6x$. Ratio residual A : B = $\frac{18x - 200}{6x} = \frac{7}{9} \implies 9(18x - 200) = 42x \implies 162x - 1800 = 42x \implies 120x = 1800 \implies x = 15$. Volume of water absorbed = $8x = 8 	imes 15 = 120	ext{ ml}$.

Mixtures and Absorption

Explanation

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