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Mixtures and Absorption

XAT 2018 · Quantitative Ability & Data Interpretation · Hard · Quantitative Aptitude

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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 medium.

  1. A.

    60 ml

  2. B.

    200/3 ml

  3. C.

    80 ml

  4. D.

    100 ml

  5. E.

    120 ml

Answer

E

Explanation

Let total mixture = 24x24x. Water = 8x8x, Liquid A = 10x10x, Liquid B = 6x6x. Medium absorbs all water (8x8x) and some amount yy of A. Total absorbed = 8x+y=200  ⟹  y=200−8x8x + y = 200 \implies y = 200 - 8x. Residual A = 10x−y=10x−(200−8x)=18x−20010x - y = 10x - (200 - 8x) = 18x - 200. Residual B = 6x6x. Ratio residual A : B = 18x−2006x=79  ⟹  9(18x−200)=42x  ⟹  162x−1800=42x  ⟹  120x=1800  ⟹  x=15\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=8×15=120 ml8x = 8 \times 15 = 120\text{ ml}.

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