Percentage Problem

[neoshichhadva]

On a certain road, 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 20% of the motorists who exceed the posted limit do not receive speeding tickets. What percent of the motorists on that road exceed the posted speed limit?

A) 10.5%
B) 12.5%
C) 15%
D) 22%
E) 30%

[spoiler]Answer: B. [/spoiler]

Can someone explain how to solve?

[shankar.ashwin]

Those who exceed speed and get no ticket = 20%

So, 80% of the people who exceed speed get tickets.

THis 80% is given as 10

So 100% (All those who exceeded) = 10/80*100 = 12.5%

[cans]

E*R=10% (Exceed speed and Receive ticket)
let x% exceed speed. thus x/5 don't get ticket. and thus 4x/5 get ticket
4x/5 = 10 or x=12.5

[Bigred2008]

What's the source?

[mehrasa]

Those who exceed speed and get no ticket = 20%

So, 80% of the people who exceed speed get tickets.

THis 80% is given as 10

So 100% (All those who exceeded) = 10/80*100 = 12.5%

good job shankar
i saw such Qs before a few times... i am wondering when we can use this method(20% get ticket ==> %80 don't get ticket) since we already have the percentage for ppl who got ticket(10%)... how it is possible that 10%=80%??????????

[shankar.ashwin]

Hi Mehrasa,

Think you misinterpreted the question.


The 10% and the 80% don't relate to the same entity.

The 10% here is 10% of the total bikers travelling (Including both who exceed speed and those who do not)

The bikers who exceed speed are further classified into those who get tickets and those who dont.

The 80% in the question relates to people who exceed speed AND get tickets (This is given to be 10% of total)

Hope this makes sense. I agree the wordings are confusing in this, but try to relate it with the solution, you should be able to understand better.

Those who exceed speed and get no ticket = 20%

So, 80% of the people who exceed speed get tickets.

THis 80% is given as 10

So 100% (All those who exceeded) = 10/80*100 = 12.5%

good job shankar
i saw such Qs before a few times... i am wondering when we can use this method(20% get ticket ==> %80 don't get ticket) since we already have the percentage for ppl who got ticket(10%)... how it is possible that 10%=80%??????????

[GMATGuruNY]

I posted a solution here:

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