1993 AMC 12 Problem 9

Question

Country

A

has

c\%

of the world’s population and owns

d\%

of the world’s wealth. Country

B

has

e\%

of the world’s population and

f\%

of its wealth. Assume that the citizens of

A

share the wealth of

A

equally, and assume that those of

B

share the wealth of

B

equally. Find the ratio of the wealth of a citizen of

A

to the wealth of a citizen of

B.

\frac{cd}{ef}

\frac{ce}{df}

\frac{cf}{de}

\frac{de}{cf}

\frac{df}{ce}

Per-capita wealth is total wealth divided by population

Form the ratio

\frac{\frac{d}{c}}{\frac{f}{e}}

Country

A

’s per-capita share is proportional to

\frac{d}{c},

while country

B

’s is proportional to

\frac{f}{e}.

Their ratio is

\frac{\frac{d}{c}}{\frac{f}{e}}=\frac{de}{cf}.

Thus the correct answer is D.

Problem 9 in other years