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# On a certain road 10 percent of the motorists exceed the

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Intern
Joined: 21 Jul 2005
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On a certain road 10 percent of the motorists exceed the [#permalink]  01 Mar 2006, 15:08
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On a certain road 10 percent of the motorists exceed the posted speed limit and receive speeding tickets, but 20 percent of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?

(A) 10 Â½ % (B) 12 1/2% (C) 15% (D) 22% (E) 30%

Kindly Explain the Ans
Manager
Joined: 01 Feb 2006
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Re: Can anybody solve the PS [#permalink]  01 Mar 2006, 16:24
psk4998 wrote:
On a certain road 10 percent of the motorists exceed the posted speed limit and receive speeding tickets, but 20 percent of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?

(A) 10 Â½ % (B) 12 1/2% (C) 15% (D) 22% (E) 30%

Kindly Explain the Ans
10% of motorists = ticketed speeders = 80% of all speeders. 10 = 80/100 x T.............T is total percent of speeders.

Solving for T you get 12.5%
GMAT Club Legend
Joined: 07 Jul 2004
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Assume:

% of motorists = 100
% who speed = x
% of motorists who does not speed = 100-x

We're told 10% of the motorists exceed the posted speed limit and receive speeding ticket. This is 10% of the total motorists.

Then we're told 20% of the motorists WHO exceed the posted speed limit do not receive speeding ticket. So, we can write:

Number of motorist who exceed speed limit and get ticket = 0.2x
This 0.2x is also equal to x-10 since we know 10% of the total motorists speed and get tickets and the total% of motorists who speed is x.

Equating, we have:
0.2x = x-10
10 = 0.8x
x = 12.5
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