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A jar full of juice contains $60 \%$ sugar. A part of this juice is replaced by another containing $22 \%$ sugar and now the percentage of sugar was found to be $42 \%$. The quantity of juice replaced is:

  1. $10/19$
  2. $9/19$
  3. $9/10$
  4. $10/9$
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Let the fraction of quantity replaced be $x$ and initial quantity be $y$.

$0.6 y - 0.6 xy + 0.22 xy = 0.42y$

$\\\implies 0.6 - 0.38x = 0.42\\\implies x = \frac{18}{38}= \frac{9}{19}$
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