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4% of the population of a certain country owns both a car

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4% of the population of a certain country owns both a car [#permalink] New post 28 Apr 2012, 18:47
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4% of the population of a certain country owns both a car and a boat. If 20% of those who own a boat, do not own a car, what percentage of the country's population owns a boat?

A. 5%
B. 7.5%
C. 10%
D. 12.5%
E. 15%
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Re: 4% of the population of a certain country owns both a car [#permalink] New post 29 Apr 2012, 02:59
Expert's post
monir6000 wrote:
4% of the population of a certain country owns both a car and a boat. If 20% of those who own a boat, do not own a car, what percentage of the country's population owns a boat?

A. 5%
B. 7.5%
C. 10%
D. 12.5%
E. 15%


Say total population of the country is 100. Then # of people who owns both a car and a boat is 0.04*100=4.

Now, since 20% of those who own a boat, do not own a car, then 80% of those who own a boat, do own a car, so own both a car and a boat. So, we have that if # of people who owns a boat is B, then # of people who owns both a car and a boat is 0.8B. On the other hand we know that # of people who owns both a car and a boat is 4, hence 0.8B=4 --> B=5. Which means that 5% of the population owns a boat.

Answer: A.
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Re: 4% of the population of a certain country owns both a car [#permalink] New post 27 Dec 2012, 20:44
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monir6000 wrote:
4% of the population of a certain country owns both a car and a boat. If 20% of those who own a boat, do not own a car, what percentage of the country's population owns a boat?

A. 5%
B. 7.5%
C. 10%
D. 12.5%
E. 15%


Let “x” be the total number of people with a boat.
Let “y” be the total population.
4% own both a boat and a car -> 0.04y ------- 1
20% of those who own a boat do not own a car
So 80% of those who own a boat own a car -> 0.8x ------2
Since 1 and 2 represent the number of people with both car and boat
0.04y = 0.8x
x= 0.05y -> 5% of entire population.
Re: 4% of the population of a certain country owns both a car   [#permalink] 27 Dec 2012, 20:44
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