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On a certain transatlantic crossing, 20 percent of a ships

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On a certain transatlantic crossing, 20 percent of a ships [#permalink] New post 25 Dec 2006, 07:23
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On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?

A. 33 1/3%
B. 40%
C. 50%
D. 60%
E. 66 2/3%

OPEN DISCUSSION OF THIS QUESTION IS HERE: on-a-certain-transatlantic-crossing-20-percent-of-a-ship-s-105277.html
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Re: PS [Percentage] [#permalink] New post 25 Dec 2006, 07:38
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johnycute wrote:
On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?
A. 33 1/3%
B. 40%
C. 50%
D. 60%
E. 66 2/3%


I get C (50%)

20% held roundtrip tix and took cars.
Let x be total on ship then above can be represented as 0.2x.
Let r be number of people who took round trip.
60% of roundtrip passengers did not take cars => 40% of r took cars
=>0.4r = 0.2x

=> r/x (asked) = 0.2/0.4 = 0.5
thus in terms of percentage, 50%
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 [#permalink] New post 25 Dec 2006, 08:53
I used venn diagram and got the same answer 50%
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 [#permalink] New post 25 Dec 2006, 09:12
My reasoning:

T: total passengers
G1: those with round-trip tickets
G2: those with cars .... etc
B: both with cars and tickets [ G1 x G2 ]

By definition: those with tickets only are [ G1 - B ]
those with cars only are [ G2 - B ]

B = 0.2 T
G1 - B = 0.6 G1 [ G1 only ]
--> B = 0.4 G1

back to our initial equation
B = 0.4 G1 = 0.2 T
G1/T = 0.2 / 0.4 = 0.5 or 50 %

Answer is C
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 [#permalink] New post 26 Dec 2006, 12:42
Got C

X*20/100 = Y*(100 -60)*/100
=> Y/X*100 = 50
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 [#permalink] New post 26 Dec 2006, 20:39
60% of people who had round trip tickets did not take their cars.
Thus, 40% of the people who had round trip tickets took their cars.
Number of people who had round trip tickets AND took their cars = 20

(40/100) * X = 20

<where X is the number of people who had round trip tickets>

X = 50.

Give me C!
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Re: PS [Percentage] [#permalink] New post 26 Dec 2006, 22:24
X = TOTAL no of passengers
y = total no of passengers with round trip tkt

then 20% of x = 40 % of y

hence reqd % = y/x * 100 = 50 %

choice C
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Re: On a certain transatlantic crossing, 20 percent of a ships [#permalink] New post 05 Jan 2013, 01:02
how to solve this using a 2 set matrix?
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Re: On a certain transatlantic crossing, 20 percent of a ships [#permalink] New post 05 Jan 2013, 04:36
Sachin9 wrote:
how to solve this using a 2 set matrix?


Check here: on-a-certain-transatlantic-crossing-20-percent-of-a-ship-s-105277.html
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Re: On a certain transatlantic crossing, 20 percent of a ships   [#permalink] 05 Jan 2013, 04:36
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