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Mixtures and Alligations Acid Solution

XAT 2010 · Quantitative Ability & Data Interpretation · Medium · Quantitative Ability

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A manufacturer has 200 litres of acid solution which has 15% acid content. How many litres of acid solution with 30% acid content may be added so that acid content in the resulting mixture will be more than 20% but less than 25%?

  1. A.

    More than 100 litres but less than 300 litres

  2. B.

    More than 120 litres but less than 400 litres

  3. C.

    More than 100 litres but less than 400 litres

  4. D.

    More than 120 litres but less than 300 litres

  5. E.

    None of the above

Answer

C

Explanation

Let xx litres of 30% solution be added. Case 1: Acid content > 20%: 15%(200)+30%(x)>20%(200+x)15\%(200) + 30\%(x) > 20\%(200 + x) 30+0.3x>40+0.2x  ⟹  0.1x>10  ⟹  x>10030 + 0.3x > 40 + 0.2x \implies 0.1x > 10 \implies x > 100 Case 2: Acid content < 25%: 15%(200)+30%(x)<25%(200+x)15\%(200) + 30\%(x) < 25\%(200 + x) 30+0.3x<50+0.25x  ⟹  0.05x<20  ⟹  x<40030 + 0.3x < 50 + 0.25x \implies 0.05x < 20 \implies x < 400 Thus, 100<x<400100 < x < 400 litres.

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