Problem Solving

Lee College insures its students for thefts up to $1000. The college makes no profit, but sets the premium to cover administrative costs of 10 per cent on an average claim of $120. If the annual premium per student is $24, what is the expected number of thefts per 100 students per year?
A)12
B)14
c)16
D)18
E)20

Thanks,

OA: D

gvosough wrote:Lee College insures its students for thefts up to $1000. The college makes no profit, but sets the premium to cover administrative costs of 10 per cent on an average claim of $120. If the annual premium per student is $24, what is the expected number of thefts per 100 students per year?
A)12
B)14
c)16
D)18
E)20

Thanks,

OA: D

Amount received from 100 students per year = 24 * 100 = 2400

If x is the number of thefts

Claim given to 100 students = 120 * x

Admin costs = 10 % of 120x = 12x

Now since the college makes no profit

2400 - 120x - 12x = 0
=> x = 18.18...

=> IMO D

The wording looks tough to me.. Might have been easy for the finance grads though..

annual premium per student is $24
So, total premium for 100 students is 2400

Now thee college charges 10 percent of it. So it charges 240.

so the amount that is claimed is 2400-240 = 2160

Average claim is 120.

So the expected number of claims is 2160/120 = 18.

Hope this helps!!

kvcpk wrote:
Now thee college charges 10 percent of it. So it charges 240.

I am not sure if this is correct. The question states 10% of claim. $24 is the premium paid.

paridhi wrote:

kvcpk wrote:
Now thee college charges 10 percent of it. So it charges 240.

I am not sure if this is correct. The question states 10% of claim. $24 is the premium paid.

I am also not sure about it.. I couldnt get the wordings completely..
May be I am right..May be I am wrong

There is something very weird about this wording...

To me, the problem is saying that the average claim is 120$.
It doesn't say that the total premium is 2400$ and that the school charges 10% of it.
It just says that the school charges a 24$ premium per student, only in order to cover the 10% fee from processing an average 120$ claim and that it makes no profit on top.

If the school charges premiums only to cover the 12$ per claim (10% of the average 120$ claim) and charges 24$ per student per year, the school expects 24=12*2, so 2 claims per student per year.
And therefore 200 claims per 100 students per year, which is not an answer choice, but the only logical conclusion I can see given the wording.

I think there is something wrong with the wording of that question, to be honest.

paridhi wrote:

gvosough wrote:Lee College insures its students for thefts up to $1000. The college makes no profit, but sets the premium to cover administrative costs of 10 per cent on an average claim of $120. If the annual premium per student is $24, what is the expected number of thefts per 100 students per year?
A)12
B)14
c)16
D)18
E)20

Thanks,

OA: D

Amount received from 100 students per year = 24 * 100 = 2400

If x is the number of thefts

Claim given to 100 students = 120 * x

Admin costs = 10 % of 120x = 12x

Now since the college makes no profit

2400 - 120x - 12x = 0
=> x = 18.18...

=> IMO D

i din understand this step -->
2400-120x-12x can you explain
tks!
Raunak

Ok I think I see the problem. The 2400$ is supposed to cover the thefts as well.
The wording, to me, makes it sound like the school "sets" the premiums to cover ONLY the administrative 10% costs, meaning it pays the claims from its pocket, which makes no sense of course...

So in this case, it' s definitely choice D. Still I find the wording slightly confusing, to be honest, probably on purpose...

raunakrajan wrote:
i din understand this step -->
2400-120x-12x can you explain
tks!
Raunak

The 2400$ is used to cover the claims as well as the 10% administrative fee, so from it you subtract the number of thefts (120x) + 10% fee per theft (12x) it can cover (leaving nothing, or = 0), and you get the number of thefts + 10% fee covered by 2400$ (100 students' premiums), which is what the college expects in number of thefts, since its goal is to charge just enough to cover the thefts + the 10% fee per theft.