Percentage word problem

[Xeb]

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

Answer is [spoiler](B)[/spoiler]

How do you get there?

[shankar.ashwin]

20% of those who exceed speed do not receive tickets

Therefore, 80% of those who exceed receive tickets.

This 80% is given to be 10% of total ( 10 percent of the motorists exceed the posted speed limit and receive speeding tickets)

80%(Exceed & Receive ticket) = 10% Total

Therefore, 100% ((Exceed & Receive ticket) = 12.5% (Total) B

[rohit_gmat]

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

Answer is [spoiler](B)[/spoiler]

How do you get there?

i plugged in numbers.... so there are 200 motorists and so 20 are speeding and get tickets (10%)
if 20% of the speeding motorists do not get tickets means that 80% of them do get tickets and 80% corresponds to the 20 motorists. 80% is 4/5
four 5s make a 20 ... so the remaining must be another 5 .. so 25 motorists correspond to 100% of the total motorists who are speeding
and so 12.5 % (25/2) of the 200 motorists are speeding.

but i guess doing the algebraic way is much easier in this Q

[GMATGuruNY]

I posted a solution here:

https://www.beatthegmat.com/i-don-t-know ... 86727.html