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Please Explain this Revenue Problem....

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Please Explain this Revenue Problem....

by mkbigmoz » Mon Apr 20, 2009 9:54 am
Cost of Ticket= $350

Distance Between Towns

Town A to Town B= 75 km
Town B to Town C= 65 km
Town A to Town C= 110 km


Fuel Cost: 0.20 per km



If in one day the plane flies from Town A to Town B and then to Town C before flying back to Town A, what rate must be charged, in dollars per kilometer, so that this company makes a profit that's 20 percent of the revenue? (Profit = Revenue − Cost)





A: $1.72 per kilometer
B: $1.84 per kilometer
C: $1.92 per kilometer
D: $2.00 per kilometer
E: $2.08 per kilometer
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by DeepakR » Mon Apr 20, 2009 6:25 pm
Total Cost CP= Cost of ticket + Cost of fuel

Cost of ticket = $350 and --- (1)
Total distance traveled = 75 + 65 + 110 = 250 km
Cost of fuel for 1km = $0.20
Hence cost of fuel for 250 km = (250 *0.20)/1=$50 --- (2)

Hence total cost CP= $350 +$ 50 = $400 ---- (A)

Now Profit = 20%Revenue and also Profit = Revenue - Cost
Hence 20%R=R-CP which gives,
CP=R-(R/5)=4R/5=$400 (From equation A)

Hence R=$500.

Now for 250km Revenue is $500
Hence for 1km Revenue = 500*1/250= $2

Ans= D.)

- Deepak
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by dumb.doofus » Mon Apr 20, 2009 9:40 pm
I find something dubious in this question.. coz you may call it "cost of ticket".. but that itself is the revenue to the company and not the cost. They are selling a ticket for $350.. and that's part of revenue.. . the only cost that the company has is of fuel.. and that is $50.

So I am really not sure what this question is looking for.. I have my doubts..
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by adt29 » Sat Jun 26, 2010 3:41 pm
Hi all,

Is there an easier and less tedious way to do this problem? Once I figured out the $50, and I knew the $250 I took a wild guess with the answer being $2 even just because the others looked like strange answers. That's probably not the best approach though! Any suggestions?

Thanks!
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by shrey3192 » Thu Nov 20, 2014 9:41 am
why have we take the third parameter i.e from "a to c"
since the ques only says from a to b and to c.
confused..

more over, what exactly does "rate" imply here?
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by [email protected] » Thu Nov 20, 2014 10:28 am
Hi shrey3192,

The prompt tells us that the plane flies from A to B then to C before flying BACK to A, so we have to account for the distance from A to C in our calculations.

In this case, the answer choices define the exact type of rate you're looking for (dollars per kilometer), although the prompt ALSO tells us exactly what we're looking for "what rate must be charged, in DOLLARS per KILOMETER..."

We're asked to calculate for a 20% profit, so here's what we have to work with:

The total distance (from A to B, B to C, then C back to A) = 250 km

The cost of the ticket = $350
The cost of the fuel = (250 km)($0.20/km) = $50
TOTAL COST = $400

Using the given formula:
Profit = Revenue - Cost

Profit = Revenue - 400

To earn a 20% profit, we can now do some algebra:

.2X = X - 400

400= .8X

500 = X

So $500 must be charged for a 250km trip...

$500/250km = $2/km

Final Answer: D

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by shrey3192 » Thu Nov 20, 2014 10:46 am
thank you for your valuable response but still not clear why have we considered the distance from "C to a"..a to b to c means a to c so why are we taking "c to a" again since it has already been taken into account while computing a to b to c. Moreover, the stem says that "before flying back to A" so why are we taking into account "c to a".(as you have mentioned while calculating total distance as 250)
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by Mathsbuddy » Thu Nov 20, 2014 11:49 am
Surely, as we are dealing with percentages, we don't actually need to use the distance figures...[question mark]. It should work with any distance!

Please ignore this. I just worked out that I missed the $350 ticket cost.
Last edited by Mathsbuddy on Thu Nov 20, 2014 12:46 pm, edited 1 time in total.
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by Mathsbuddy » Thu Nov 20, 2014 12:23 pm
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Last edited by Mathsbuddy on Thu Nov 20, 2014 12:47 pm, edited 1 time in total.
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by [email protected] » Thu Nov 20, 2014 12:26 pm
Hi shrey3192,

It sounds like you might be misinterpreting the prompt. Try thinking of it in these terms:

The plane made 3 flights:
1st, from Town A to Town B = 75km traveled
2nd, from Town B to Town C = 65km traveled
3rd, from Town C BACK to Town A = 110km traveled

In that 3rd flight, I have to assume that the plane is going DIRECTLY from Town C to Town A (and not back through Town B).

Total Distance = 75 + 65 + 110 = 250km

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by Mathsbuddy » Thu Nov 20, 2014 12:37 pm
shrey3192 wrote:thank you for your valuable response but still not clear why have we considered the distance from "C to a"..a to b to c means a to c so why are we taking "c to a" again since it has already been taken into account while computing a to b to c. Moreover, the stem says that "before flying back to A" so why are we taking into account "c to a".(as you have mentioned while calculating total distance as 250)
Hi Shrey,

I see what you mean. However, it's all in how you read the punctuation of the question:

1) "...from Town A to Town B and then to Town C. Before flying back to Town A, what rate..." would indeed mean just A to B to C, as you mention.
2) "...from Town A to Town B and then to Town C before flying back to Town A, what rate..." means that "before flying back to A, a plane flew from A to B to C", so A to B to C to A is ALL included.

Can you see now that there is a difference. "...before flying back to A" just means "...and then flew back to A". Nonetheless, it doesn't state "STRAIGHT back to A", so the question could be interpreted as "A to B to C to B to A". There is maybe scope for this ambiguity, particularly if it must travel on as fixed route, like a bus that visits all bus stops!
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by Mathsbuddy » Thu Nov 20, 2014 12:44 pm
Mathsbuddy wrote:Total distance, d = 75 + 65 + 110 = 250
Cost, C = 250 x 0.20 = 50
Profit, P = 0.2R where R = Revenue

P = R - C
0.2R = R - 50
0.8R = 50
R = 50/0.8 = 250/4
R/d = (250/4)/250 = 0.25
Answer = $0.25 per km (Not an answer choice!)

In fact, let's do this again without knowing distance d:

C = 0.2d
P = 0.2R

P = R - C
0.2R = R - 0.2d
0.8R = 0.2d
R = 0.2d/0.8 = d/4
R/d = 0.25
Answer = $0.25 per km (Not an answer choice!)

So, from my reckoning, you don't even need to know the distance as it's a simple percentage problem.
However, I do struggle to see why the answer should be $2.00

Could somebody please understand my workings and explain how I must have misinterpreted the question...

Thanks
Just saw my mistake. The total cost of the ticket $350 was hidden off the top of my screen. (Scroll bars drive me nuts!)
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by Mathsbuddy » Thu Nov 20, 2014 12:45 pm
Here's my correction:

Cost, C = 350 + 250 x 0.20 = 400
Profit, P = 0.2R where R = Revenue

P = R - C
0.2R = R - 400
0.8R = 400
R = 400/0.8 = 500
R/d = 500/250 = 2
Answer = $2 per km
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