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In a country, 4% of the population owns both a car and a boat. If 20%

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AnkitK
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In a country, 4% of the population owns both a car and a boat. If 20% [#permalink] New post   Updated on: 29 Apr 2023, 10:29
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In a country, 4% of the population owns both a car and a boat. If 20% of boat owners do not have a car, what percentage of the country's population owns a boat?

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

M05-12

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A

Originally posted by AnkitK on 16 Jul 2011, 08:55.
Last edited by Bunuel on 29 Apr 2023, 10:29, edited 2 times in total.
Renamed the topic and edited the question.
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Bunuel
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Re: In a country, 4% of the population owns both a car and a boat. If 20% [#permalink] New post   29 Apr 2012, 03:59
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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's assume the total population of the country is 100. In this case, the number of people who own both a car and a boat is \(0.04*100 = 4\).

Since 20% of boat owners do not own a car, it follows that 80% of boat owners do own a car, and therefore own both a car and a boat. If we denote the number of people who own a boat as B, then the number of people who own both a car and a boat is 0.8B. We know that there are 4 people who own both a car and a boat, so \(0.8B = 4\). From this, we can calculate that \(B = 5\). This means that 5% of the population owns a boat.


Answer: A
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Re: In a country, 4% of the population owns both a car and a boat. If 20% [#permalink] New post   16 Jul 2011, 09:03
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0.04x has B+C ( x is total population)

Let # of people who own a boat = y

20% of those who own a boat, do not own a car

=> 0.2y do not have a car

=> 80% of those who own a boat own a car

=> 0.8y = 0.04x

=> y/x = 4/80

So %age = 4/80 * 100 = 5%

Answer - A
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Re: In a country, 4% of the population owns both a car and a boat. If 20% [#permalink] New post   16 Jul 2011, 10:46
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for such Q's visualization may be tricky sometimes, I would recommend to use 2 * matrix here (this method is quite useful- just give it a shot)

lets say X is the % of population with a boat then you would get the equation-

4+ 0.2 * X = X -> solving this results X= 5% (here visualization is the important point!)

Hope it helps
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Re: In a country, 4% of the population owns both a car and a boat. If 20% [#permalink] New post   24 Jul 2014, 01:32
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Refer diagram below:

4% has both boat & car

20% of those who own a boat, do not own a car; it also means 80% of those who own a boat also own a car

\(\frac{80}{100} b = 4\)

b = 5
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Re: In a country, 4% of the population owns both a car and a boat. If 20% [#permalink] New post   19 Jan 2016, 21:44
hi paresh gmat, I used the same venn diagram but I got 76 people who owned car but not boat. but as 20 is the number of people who only owns boat but not car, then 20/100 should be 20%? Am I missing something.
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Re: In a country, 4% of the population owns both a car and a boat. If 20% [#permalink] New post   19 Jan 2016, 23:02
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alice7 wrote:
but I got 76 people who owned car but not boat. but as 20 is the number of people who only owns boat but not car, then 20/100 should be 20%? Am I missing something.



How did you get the underlined part?
You are given that 20% of those who owned a boat did not own a car. So 80% of total boat owners were also car owners. This is the overlap region which has 4 people. The 4 people account for 80% of total boat owners.

4 = (80/100) * Total boat owners

Total boat owners = 5
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Re: In a country, 4% of the population owns both a car and a boat. If 20% [#permalink] New post   20 Jan 2016, 13:24
SO If you assume total as 100. And 4 is the no which has both and 20 is only car. then 100-20-4 = 76 people who has only boat.
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Re: In a country, 4% of the population owns both a car and a boat. If 20% [#permalink] New post   20 Jan 2016, 23:33
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alice7 wrote:
SO If you assume total as 100. And 4 is the no which has both and 20 is only car. then 100-20-4 = 76 people who has only boat.



"If 20% of those who own a boat, do not own a car,"
does not imply that 20 people own only boat. It implies that 20% of people who own a boat do not have a car. So if 10 people own a boat, 2 of them do not have a car. If 50 people own a boat, 10 of them do not have a car. If 100 people own a boat, 20 of them do not have a car etc.
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Re: In a country, 4% of the population owns both a car and a boat. If 20% [#permalink] New post   21 Feb 2024, 05:21
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Re: In a country, 4% of the population owns both a car and a boat. If 20% [#permalink]
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