Competition problem — Combinatorics

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Combinatorics Difficulty 3.2 AMC 10/12 Find the answer

An urn is filled with coins and beads, all of which are either silver or gold. Twenty percent of the objects in the urn are beads. Forty percent of the coins in the urn are silver. What percent of objects in the urn are gold coins?
$\text{(A) } 40\%$ $\text{(B) } 48\%$ $\text{(C) } 52\%$ $\text{(D) } 60\%$ $\text{(E) } 80\%$

Your answer

Multiple choice: answer with the letter of the option you want.

Solution

If twenty percent of the objects in the urn are beads, then the other $80$ % of the objects must be coins. Since $40$ % of the coins are silver, then $60$ % of the coins must be gold. Therefore, $60$ % of $80$ % of the objects in the urn are gold coins. Since $.6\times.8=.48$ , 48 percent of the objects in the urn must be gold coins. Thus the answer is $\fbox{B}$ .

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.