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2013 Math Kangaroo

Problem 10

Problem 10 · 2013 Math Kangaroo Medium
Fractions, Decimals & Percents percent-multiplier

When a certain substance melts, its volume increases by 112. By what fraction does the volume decrease when the substance solidifies again?

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Answer: D113
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Hint 1 of 2
The increase and the decrease are measured against different totals.
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Hint 2 of 2
Find the fraction of the larger (melted) volume that must disappear to return to the start.
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Approach: fraction of the new total
  1. Start with volume V; melted volume is V(1 + 1/12) = 13V/12.
  2. To return to V it must lose V/12.
  3. As a fraction of 13V/12 that is (V/12)/(13V/12) = 1/13, so D.
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