Complex Estimations - CCAT Test Prep

This type of question tests your ability to calculate percentage changes in revenue based on different pricing strategies. Understanding how a price change affects sales and revenue can be very useful in business scenarios, such as setting ticket prices or product pricing to maximize profit. We'll break it down step by step to make the solution clear.

How to Calculate Revenue Increase Step-by-Step

Question 1 - Percentage Increase in Revenue

A basketball team knows that it can sell all 1,000 seats in its arena for a price of $15, but determines that if it sells tickets for $20, then it will only sell 90% of the seats. By what percentage will the team increase its revenue if it decides to sell tickets for the higher price?

A) 10%
B) 12%
C) 15%
D) 18%
E) 20%

Understand the Problem

At the $15 price, 1,000 seats can be sold.
At the $20 price, only 90% of seats can be sold, meaning 900 seats.

Step 1: Calculate the Original Revenue

Revenue from selling tickets at $15 each:

Revenue at $15 
    = 15 × 1,000
    = $15,000

Step 2: Calculate the New Revenue at $20

Revenue from selling 90% of the seats (900 seats) at $20:

Revenue at $20 
    = 20 × 900
    = $18,000

Step 3: Find the Difference in Revenue

Difference between new and original revenue:

Difference in Revenue 
    = 18,000 - 15,000
    = $3,000

Step 4: Calculate the Percentage Increase

To calculate the percentage increase in revenue:

Percentage Increase 
    = (Difference in Revenue / Original Revenue) × 100
    = (3,000 / 15,000) × 100
    = 20%

Answer: 20%

Question 2 - Decrease in Revenue

A concert venue normally sells 800 tickets at $25 each. The ticket price is reduced to $20, and ticket sales rise to 900. By what percentage will the revenue change?

A) -5%
B) 0%
C) 5%
D) 10%
E) 15%

Understand the Problem

Initially, the ticket price is $25 with 800 tickets sold.
After reducing the price to $20, 900 tickets are sold.

Step 1: Calculate the Original Revenue

Revenue from selling 800 tickets at $25 each:

Revenue at $25 
    = 25 × 800
    = $20,000

Step 2: Calculate the New Revenue at $20

Revenue from selling 900 tickets at $20 each:

Revenue at $20 
    = 20 × 900
    = $18,000

Step 3: Find the Difference in Revenue

Difference between new and original revenue:

Difference in Revenue 
    = 18,000 - 20,000
    = -$2,000

Step 4: Calculate the Percentage Decrease

To calculate the percentage decrease in revenue:

Percentage Decrease 
    = (Difference in Revenue / Original Revenue) × 100
    = (-2,000 / 20,000) × 100
    = -10%

Answer: -10%

Question 3 - No Change in Revenue

A gym initially has 500 members paying $50 each for a monthly membership. After raising the price to $60, membership drops to 420 members. By what percentage will the revenue change?

A) -5%
B) 0%
C) 5%
D) 10%
E) 12%

Understand the Problem

Initially, the membership is $50 with 500 members.
After raising the price to $60, 420 members remain.

Step 1: Calculate the Original Revenue

Revenue from 500 members at $50 each:

Revenue at $50 
    = 50 × 500
    = $25,000

Step 2: Calculate the New Revenue at $60

Revenue from 420 members at $60 each:

Revenue at $60 
    = 60 × 420
    = $25,200

Step 3: Find the Difference in Revenue

Difference between new and original revenue:

Difference in Revenue 
    = 25,200 - 25,000
    = $200

Step 4: Calculate the Percentage Increase

To calculate the percentage increase in revenue:

Percentage Increase 
    = (Difference in Revenue / Original Revenue) × 100
    = (200 / 25,000) × 100
    = 0.8%

Answer: 0.8%

How to Solve These Questions Easily

Calculate Original and New Revenues: Calculate the revenue for both the original and the new prices.
Find the Difference: Determine whether the difference is an increase or decrease.
Calculate the Percentage: Use the formula to calculate the percentage change relative to the original revenue.

This step-by-step approach makes it easier to solve these types of problems, even when dealing with changes in price and sales.

20 Practice Questions - Revenue Change Calculations

A shop sells 500 items at $12 each. If the price is raised to $15 and only 400 items are sold, what is the percentage change in revenue?

A) -8%
B) -5%
C) 0%
D) 5%
E) 8%

A farmer sells 800 bags of apples at $8 each. If the price increases to $10 and only 600 bags are sold, what is the percentage change in revenue?

A) -10%
B) -5%
C) 0%
D) 5%
E) 10%

A movie theater sells 1,000 tickets at $10 each. If they raise the ticket price to $12 but sell only 850 tickets, what is the percentage change in revenue?

A) -2%
B) 0%
C) 2%
D) 5%
E) 10%

A gym membership is priced at $60 for 150 members. If the price is increased to $70 and the number of members drops to 120, what is the percentage change in revenue?

A) -8%
B) -5%
C) 0%
D) 5%
E) 8%

A school fundraiser sells 200 tickets at $25 each. If they increase the price to $30 and sell only 150 tickets, what is the percentage change in revenue?

A) -10%
B) -5%
C) 0%
D) 5%
E) 10%

A football stadium sells 5,000 tickets at $30 each. If the price is reduced to $25 and attendance rises to 5,500, what is the percentage change in revenue?

A) -2%
B) 0%
C) 2%
D) 5%
E) 10%

A concert sells 2,000 tickets at $50 each. If the price is reduced to $45 and 2,500 tickets are sold, what is the percentage change in revenue?

A) 8%
B) 10%
C) 12%
D) 14%
E) 16%

A charity event sells 300 tickets for $20 each. If the price is increased to $25 but only 250 tickets are sold, what is the percentage change in revenue?

A) -5%
B) 0%
C) 5%
D) 8%
E) 10%

A restaurant sells 1,200 meals at $15 each. If the price is increased to $18 and only 1,000 meals are sold, what is the percentage change in revenue?

A) 0%
B) 2%
C) 4%
D) 6%
E) 8%

A football club sells 4,000 tickets at $25 each. If the ticket price is increased to $28, and sales drop to 3,200 tickets, what is the percentage change in revenue?

A) -5%
B) 0%
C) 5%
D) 8%
E) 10%

A carnival sells 1,500 tickets at $8 each. If the price is reduced to $7 and ticket sales rise to 2,000, what is the percentage change in revenue?

A) 2%
B) 5%
C) 8%
D) 10%
E) 12%

A zoo sells 1,000 tickets at $15 each. If the ticket price is reduced to $12 and 1,500 tickets are sold, what is the percentage change in revenue?

A) -2%
B) 0%
C) 2%
D) 5%
E) 8%

A theater sells 800 seats at $20 each. If the price is raised to $22 but only 700 seats are sold, what is the percentage change in revenue?

A) -4%
B) -2%
C) 0%
D) 2%
E) 5%

A baseball game sells 6,000 tickets at $10 each. If the price is increased to $12 and only 5,000 tickets are sold, what is the percentage change in revenue?

A) -5%
B) 0%
C) 5%
D) 10%
E) 12%

A swimming pool sells 1,200 entries at $6 each. If the price is reduced to $5 and attendance rises to 1,400, what is the percentage change in revenue?

A) -5%
B) 0%
C) 5%
D) 8%
E) 10%

A museum sells 1,000 tickets at $30 each. If the price is increased to $35 and only 800 tickets are sold, what is the percentage change in revenue?

A) -10%
B) -5%
C) 0%
D) 5%
E) 8%

A dance show sells 2,000 tickets at $25 each. If the price is reduced to $20, and ticket sales rise to 2,500, what is the percentage change in revenue?

A) 2%
B) 5%
C) 8%
D) 10%
E) 12%

A gym sells 300 memberships at $40 each. If the price is reduced to $35 and 350 memberships are sold, what is the percentage change in revenue?

A) -5%
B) 0%
C) 5%
D) 10%
E) 12%

A stadium sells 10,000 tickets at $15 each. If the price is raised to $18, and 8,500 tickets are sold, what is the percentage change in revenue?

A) -10%
B) -5%
C) 0%
D) 5%
E) 10%

A music festival sells 3,000 tickets at $50 each. If the ticket price is increased to $55 and ticket sales drop to 2,600, what is the percentage change in revenue?

A) -8%
B) -5%
C) 0%
D) 5%
E) 8%

Answers to Practice Questions

C) 50%
D) 35%
A) 20%
C) 60%
B) 30%
A) 25%
E) 40%
B) 30%
D) 45%
C) 36%
B) 20%
D) 40%
E) 30%
C) 25%
A) 15%
B) 35%
E) 50%
D) 45%
A) 10%
C) 25%

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