If an organization were to sell n tickets for a theater production, th

Question

If an organization were to sell n tickets for a theater production, the total revenue from ticket sales would be 20 percent greater than the total costs of the production. If the organization actually sold all but 5 percent of the n tickets, the total revenue from ticket sales was what percent greater than the total costs of the production?

(A) 4%
(B) 10%
(C) 14%
(D) 15%
(E) 18%

(A) 4% 
(B) 10% 
(C) 14%
(D) 15% 
(E) 18%

ScottTargetTestPrep · Accepted Answer

If we let c = the total cost of production, then 1.2c = the revenue from selling n tickets. Another way of saying this is that selling n tickets results in 1.2c. But we want to determine the total revenue from selling 95% of the tickets, or 0.95n. If we let x = the total revenue from selling 95% of the tickets, we can create the proportion:

n/1.2c = 0.95n/x

nx = (1.2c)(0.95n)

nx = 1.14nc

x = 1.14c

The total revenue from selling 95% of the tickets is 1.14c, which means that the total revenue is 14% greater than the cost of production.

Answer: C

Kurtosis · Answer

Let n = 100; Price of each ticket = 12
Cost = (Revenue)/1.2 = (100*12)/1.2 = 1000

Suppose the organization sold all but 5% of tickets i.e. 95 tickets, then revenue = 95*12

Percentage required = ((95*12 - 1000)/1000)*100 = (1140 - 1000)/10 = 14%

Answer: C

kris19 · Answer

revenue for n tickets = 1.2*(total costs of production), take total costs = c
asking what is the revenue for 0.95n tickets ?
I reasoned it as: for n tickets-> 1.2c, then for 0.95n tickets-> what c? taking the cross-multiplication we get = 1.2*0.95 = 1.14c, it means revenue is 14% greater than production costs.

IdiomSavant · Answer

Pick numbers. 
N= 20
Cost = $100
Revenue +20% = $120

Results of numbers picked. 
Unit price of N = $6
N - 5% = 19 tickets
New revenue = 19 * 6 =114
Cost 100, new revenue 114, increase 14%

2020MBA · Answer

Simple ratio problem here.

100/120 = 95/x. x = 114, or 14% greater than cost.

TimeTraveller · Answer

n = 1.2p 
 0.95n = xp

x = \frac{0.95n * 1.2p}{pn} = 0.95 * 1.2 = 1.14 = 14% . Ans - C.

dave13 · Answer

Toal numbet of tickets = 100
Cost per ticket = 1 EUR
Total cost = 100 EUR
Selling price = 1.2 EUR
Total revenu = 120

BUT
Sold 95 Tickets
Total revenue 95*1.2 = 114

so,  \frac{(114-100)}{100} *100% = 14

Fdambro294 · Answer

You can use a simple proportion equation.

Quantity or tickets sold is directly proportional the “percent greater” than the Total Costs

Let C = Total Costs

100% * (N) ———————> 120% * (C)

95% * (N) ———————> (P %) * (C)

120% (C) * (95% / 100%) = P%

1.2 * .95 = 1.14 ———-> or 114% of Total Costs

Which is 14% greater

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Nijhumimtiyaz134 · Answer

Let, 
Total cost= 100
Hence, revenue is 120

Let, the price of ticket is $1
Hence ticket sold is 120

If, 5% ticket is unsold, then the number of ticket sold is 114. Hence revenue is 14. Which is 14%. 🙂

Posted from my mobile device

Ghoskrp3 · Answer

The easiest approach was not highly mathematical actually, although I wasted my 5mins initially but when I looked closely the answer came out in 20 sec, so here it goes ...

firstly 100% of ticket sales yield ----------------------------> 120% of total production cost then the say they sold all but 5% of the tickets, which means 95% sale actually happened -------------------> X% of total production cost (which is what we need to find) Since if they would have sold all the tickets their total revenue would have been ------------------> 120% (as given) as they sold only 95%, which tells they made 95% of 120% of the revenue ------------------> so since 10% of 120% is 12%, so 5% of 120% would be 6% => so that means 95% of 120% => 120% - 6% = 114%, so profit slipped from 20% to 14% due to the reduced tickets sale ... Hence Answer is E) 14%

siddhantvarma · Answer

Let:
n = total number of tickets available
p = price per ticket
C = total costs of production

From the first condition, when all n tickets are sold: Total revenue = n × p = 1.2C (20% greater than costs)

From the second condition, when 95% of tickets are sold: New total revenue = 0.95n × p

Substituting n x p as 1.2C in the second equation: 0.95n × p = 0.95 × (1.2C) = 1.14C

This means the new revenue is 14% greater than the costs.
Therefore, the answer is (C) 14%.

vikalpjain91 · Answer

Answer is C, Please find explanation below:
Let us suppose,

1$ = 1 Ticket
100 Tickets are there

Now equation will become:
Tickets: 100
Therefore, CP: 100
and as given, SP: 120

Now if 95 percent tickets were sold
Tickets: 95
CP: 100 which is actually fixed
New SP = 95*1.2 / 100 => 114/100 => 14%

Answer is C

steffe440 · Answer

For this one I just did the revenue which I call r will be 20% greater than the cost, hence the revenue will be r = 1.2c , so the profit would be 1.2c - c, and let's say the cost is 100 units. Then we would have 120 units - 100 units, and we know that 5% of the revenue will not be cashed in, hence only 114 units will be sold, hence we have: 114-100, or 14 units of profit instead of 20 units of profit

If an organization were to sell n tickets for a theater production, th

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If an organization were to sell n tickets for a theater production, th

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