test30 # 16

[dunkin77]

Hi,

The answer is B) but I don't seem to translate word into equation.... Can anyone please help?

[f2001290]

Let 'T' be the total no. of motorists on the road.
Let E(R) be the no. of motorists who exceed the speed and receive tickets.
Let E(~R) be the no. of motorists who exceed the speed limit but doesn't receive tickets.
Let 'E' be the no. of motorists who exceed speed.
=> E = E(R) + E(~R)

From statement (1)
-> E(R) = (10/100)* T
From statement (2)
-> E(~R) = (20/100)*E
E(~R) = (20/100)*(E(R) + E(~R))
E(~R) = (1/4)*E(R)

Using both the equations, find out
E(R) + E(~R)/T

[Cybermusings]

Let the total number of motorists on the road be x
Now 10x/100 or x/10 motorists exceed speed limits and also receive tickets
Now out of the total number of people who exceed speed limits (say y)...20% exceed speed limits and do not receive tickets...thus people who do speed and get tickets = 80y/100 or x/10
So 8y/10 = x/10
or y = 10x/80

So % of speed limit offenders = (10x/80)/x * 100
= 1000/80
= 100/8 = 12.5%