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

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.

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%

Simple ratio problem here.

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

\(n = 1.2p\)
\(0.95n = xp\)

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

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

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

Posted from my mobile device

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

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%­

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%.

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