Tommy's office organizes company trips from its employees. The company

Question

Tommy's office organizes company trips from its employees. The company allows employees to register for the trip for a down payment of $63, a 10% markup over the amount the company spends per person on this trip. If employees change their minds, they can cancel their registration but will receive only a 90% refund on their payment. If 100 people registered for the trip but 50 canceled, and if the company does not spend money on canceled registrations, then what was Tommy's office's approximate profit or loss on the trip as a percentage of their total expenses?

A. 15% loss
B. 20% loss
C. 10% profit
D. 15% profit
E. 20% profit

A. 15% loss
B. 20% loss
C. 10% profit
D. 15% profit
E. 20% profit

chetan2u · Answer

Quick thinking: The minimum profit is 10% if all went. The profit % will keep increasing as more cancellations are done. For example if all cancel the profit percentage is infinite as the profit is over ZERO expenditure. 
Thus only D and E are left.  
10% was the profit on markup price of 63.
But the remaining 50 too are giving 10% of actual cost as profit without any excess expenditure. Thus 10%+10% over the actual expenditure of 50 person. 
Answer : 20%

Arithmetic  
110% of the actual cost = 63, so actual cost =  63*\frac{100}{110} .
Since 50 employees went for the trip, the actual cost =  \frac{6300}{110}*50=\frac{6300*5}{11}

The profit per person is 10% of actual cost, so profit for all 100 person =  63*\frac{100}{110}*\frac{10}{100}*100=\frac{6300}{11}

Profit % =  \frac{\frac{6300}{11}}{\frac{6300*5}{11}}*100=20

E

Tung204 · Answer

Why didn’t we take into account the 90% refund for the cancelled registration and assume that “does not spend money on cancelled registration” means no-refund also?

Posted from my mobile device

marcraphaelmatta · Answer

I was confused by one thing: 63 dollars is a downpayment ( constitutes 10 % markup)
==> therefore, we cannot conclude that 1.1 *CP= 63
I concluded that 63 dollars are the profit of the company as 63 dollars is 10 % markup on the cost
63=0.1 COST 
cost =630

QuantMadeEasy · Answer

Solution:

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hoooplaa · Answer

I seriously doubt the answer to be correct over here. The point being, the fact that the employees who cancel receive back 90% of the MARKED UP price, and not 90% of the cost, has been overlooked.

Here is the math that can prove my point.

Does the $63 figure really matter? If it had been any other number, would your answer change? Why not keep the numbers simple. If you agree to say NO with me, please read on.

Let the cost to company of the trip be $100. Then, the cost incurred is $5000. SIMPLE.

People who actually went, have paid 50×$110 = $5500

People who did not go also paid $110 each, but were only returned 90% of that viz. $99 each. Hence, the company kept $11 in its pocket. It is this number which is $11 instead of $10 per person, which makes my answer different which is not even in the options. Hence, revenue earned from them is effectively 50×$11 = $550

Total Revenue = $5500 + $550 = $6050

Total profit = $1050 = 21% of Total Cost

I rest my case.

Krunaal · Answer

Your analysis is absolutely right. However, the question specifies an  approximation , and  E. 20% profit  is the closest provided option. Given that 21% is just 1% higher, it can be reasonably rounded down to  20%  as an approximate value.

Tommy's office organizes company trips from its employees. The company

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