Bunuel wrote:
Tough and Tricky questions: Word Problems.
In a rare coin collection, one in six coins is gold, and all coins are either gold or silver. If 10 silver coins were to be subsequently traded for an additional 10 gold coins, the ratio of gold coins to silver coins would be 1 to 4. Based on this information, how many gold coins would there be in this collection after the proposed trade?
A) 50
B) 60
C) 180
D) 200
E) 300
Kudos for a correct solution.Source: Chili Hot GMAT
1. Original ratio, where all coins are gold or silver, and one in six coins is gold (other 5 are silver)
\(\frac{G}{S}\) = \(\frac{1x}{5x}\)
2. Ten silver coins are traded for ten gold coins, and the new ratio of gold coins to silver coins is 1 to 4:
\(\frac{x + 10}{5x -
10}\) = \(\frac{1}{4}\)
4(x + 10) = 5x - 10
4x + 40 = 5x - 10
x = 50 -- that's the multiplier
Originally there were 1x = 50 gold coins; after the trade, there are 10 more. Total is 60.
Answer B
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