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Real estate math: percentages, area, and profit and loss
Finish →Question 1 of 40
Which equation finds a percentage rate when the part and whole are known?
Reveal answer
Correct answer: Part divided by whole
Divide part by whole to obtain the decimal rate, then multiply by 100 to express it as a percent.
Question 2 of 40
A buyer pays 12% of a $250,000 purchase price as a down payment. What is the down payment?
Reveal answer
Correct answer: $30,000
Convert 12% to 12 ÷ 100 = 0.12. Multiply $250,000 × 0.12 = $30,000.
Question 3 of 40
A $21,000 commission equals 6% of a property's sales price. What was the sales price?
Reveal answer
Correct answer: $350,000
The commission is the part. Convert 6% to 0.06. Price = $21,000 ÷ 0.06 = $350,000. Check: $350,000 × 0.06 = $21,000.
Question 4 of 40
How many square feet are in one acre?
Reveal answer
Correct answer: 43,560
One acre equals 43,560 square feet. The other common conversion factors describe different units or contain a decimal-place error.
Question 5 of 40
A rectangular lot is 80 feet wide and 125 feet deep. What is its area?
Reveal answer
Correct answer: 10,000 square feet
Rectangle area = length × width = 125 feet × 80 feet = 10,000 square feet.
Question 6 of 40
A parcel bought for $180,000 is sold for $216,000. Ignoring all expenses, what is the profit percentage on cost?
Reveal answer
Correct answer: 20%
Profit = $216,000 − $180,000 = $36,000. Profit on cost = $36,000 ÷ $180,000 = 0.20 = 20%.
Question 7 of 40
A property costs $240,000 and sells for $300,000, with no expenses. One analyst reports a 25% profit on cost; another reports a 20% margin on selling price. Which assessment is correct?
Reveal answer
Correct answer: Both are correct because they use different stated denominators.
Profit = $300,000 − $240,000 = $60,000. On cost: $60,000 ÷ $240,000 = 0.25 = 25%. On selling price: $60,000 ÷ $300,000 = 0.20 = 20%. Each rate correctly answers its stated question.
Question 8 of 40
Under Florida Statutes section 475.705, how may the commission amount be expressed in a commercial real estate commission notice?
Reveal answer
Correct answer: As a dollar amount or a formula, such as a percentage of sales price
Fla. Stat. § 475.705(1)(e) allows a dollar amount or a formula determining the amount, including a percentage of sales price.
Question 9 of 40
A triangular parcel has a 180-foot base and a perpendicular height of 120 feet. What is its area?
Reveal answer
Correct answer: 10,800 square feet
Triangle area = base × perpendicular height ÷ 2. Thus 180 × 120 = 21,600; 21,600 ÷ 2 = 10,800 square feet.
Question 10 of 40
A tract contains 108,900 square feet. How many acres is that?
Reveal answer
Correct answer: 2.5 acres
Acres = square feet ÷ 43,560. Thus 108,900 ÷ 43,560 = 2.5 acres.
Question 11 of 40
A 3-acre parcel sells for $2 per square foot. What is the total price?
Reveal answer
Correct answer: $261,360
Convert area: 3 × 43,560 = 130,680 square feet. Multiply by unit price: 130,680 × $2 = $261,360.
Question 12 of 40
Which expression gives the selling price needed for a specified profit percentage on cost, assuming no other expenses?
Reveal answer
Correct answer: Cost × (1 + decimal profit rate)
Selling price must recover cost plus the profit. Cost + cost × rate = cost × (1 + rate).
Question 13 of 40
An investor sells land for $276,000 at a 15% profit on original cost. No other expenses apply. What was the original cost?
Reveal answer
Correct answer: $240,000
15% = 0.15; selling price = cost × (1 + 0.15) = cost × 1.15. Cost = $276,000 ÷ 1.15 = $240,000.
Question 14 of 40
Land sells for $153,000 after a 10% loss on cost. Ignoring expenses, what was its cost?
Reveal answer
Correct answer: $170,000
10% = 0.10. The retained percentage is 1 − 0.10 = 0.90. Cost = $153,000 ÷ 0.90 = $170,000.
Question 15 of 40
An owner's property value rises 10% and then falls 10% from the increased value. Relative to the starting value, what is the result?
Reveal answer
Correct answer: A 1% loss
Use a starting index of 100. Increase: 100 × 1.10 = 110. Decrease: 110 × 0.90 = 99. Loss = 100 − 99 = 1; 1 ÷ 100 = 0.01 = 1%.
Question 16 of 40
A rectangular parcel measures one-half mile by 660 feet. How many acres does it contain?
Reveal answer
Correct answer: 40 acres
Convert length: 0.5 × 5,280 = 2,640 feet. Area = 2,640 × 660 = 1,742,400 square feet. Acres = 1,742,400 ÷ 43,560 = 40.
Question 17 of 40
An L-shaped parcel consists of a 200-foot by 150-foot rectangle with a 50-foot by 60-foot corner excluded. What is the parcel's area?
Reveal answer
Correct answer: 27,000 square feet
Full rectangle = 200 × 150 = 30,000 square feet. Excluded corner = 50 × 60 = 3,000 square feet. Parcel = 30,000 − 3,000 = 27,000 square feet.
Question 18 of 40
A 90-foot by 140-foot rectangular lot must be fenced along all four sides, with no openings. How many linear feet of fencing are needed?
Reveal answer
Correct answer: 460 feet
Perimeter = 2 × (90 + 140) = 2 × 230 = 460 linear feet.
Question 19 of 40
A $480,000 sale earns a 5% total commission. The listing brokerage receives 60% of that commission, and its sales associate receives 70% of the listing brokerage's share. What does the associate receive?
Reveal answer
Correct answer: $10,080
Total commission = $480,000 × 0.05 = $24,000. Listing brokerage share = $24,000 × 0.60 = $14,400. Associate share = $14,400 × 0.70 = $10,080.
Question 20 of 40
An associate receives 75% of her brokerage's share. Her brokerage receives 40% of the total commission. What percentage of the total commission does she receive?
Reveal answer
Correct answer: 30%
Convert the shares to decimals: 75% = 0.75 and 40% = 0.40. Combined share = 0.75 × 0.40 = 0.30 = 30% of total commission.
Question 21 of 40
For a simple resale with no expenses, which expression gives the dollar loss when selling price is below cost?
Reveal answer
Correct answer: Cost minus selling price
The positive dollar amount of a loss is cost minus selling price. Division produces a ratio, not the dollar shortfall.
Question 22 of 40
A property purchased for $320,000 sells for $272,000. Ignoring expenses, what is the percentage loss on cost?
Reveal answer
Correct answer: 15%
Loss = $320,000 − $272,000 = $48,000. Loss rate = $48,000 ÷ $320,000 = 0.15 = 15%.
Question 23 of 40
An investor pays $150,000 for property and spends $20,000 on improvements. The property sells for $200,000 with $12,000 in selling expenses. What is the dollar profit after these costs?
Reveal answer
Correct answer: $18,000
Investment cost = $150,000 + $20,000 = $170,000. Net sale receipts = $200,000 − $12,000 = $188,000. Profit = $188,000 − $170,000 = $18,000.
Question 24 of 40
An owner paid $180,000 for property, sells it for $250,000, pays $10,000 in selling expenses, and repays $100,000 of loan principal at closing. Ignoring all other costs, which pair correctly shows profit and closing cash proceeds?
Reveal answer
Correct answer: Profit $60,000; cash proceeds $140,000
Net sale receipts = $250,000 − $10,000 = $240,000. Profit = $240,000 − $180,000 = $60,000. Closing cash = $240,000 − $100,000 principal payoff = $140,000. Principal payoff affects cash but is not another purchase-cost expense.
Question 25 of 40
A standard survey section contains how many acres?
Reveal answer
Correct answer: 640 acres
A standard section is one square mile and contains 640 acres.
Question 26 of 40
What is the acreage of the north half of the southeast quarter of a standard 640-acre section?
Reveal answer
Correct answer: 80 acres
The southeast quarter contains 640 ÷ 4 = 160 acres. Its north half contains 160 ÷ 2 = 80 acres.
Question 27 of 40
A rectangular strip measures 30 yards by 120 feet. Using 3 feet per yard, what is its area in square feet?
Reveal answer
Correct answer: 10,800 square feet
Convert 30 yards × 3 feet per yard = 90 feet. Area = 90 × 120 = 10,800 square feet.
Question 28 of 40
A $225,000 parcel contains 1.5 acres. What is its price per square foot, rounded to the nearest cent?
Reveal answer
Correct answer: $3.44
Area = 1.5 × 43,560 = 65,340 square feet. Unit price = $225,000 ÷ 65,340 ≈ $3.443526 per square foot. Rounded to cents: $3.44.
Question 29 of 40
Parcel A costs $120,000 for 20,000 square feet. Parcel B costs $150,000 for 30,000 square feet. Based solely on price per square foot, which is less expensive and by how much?
Reveal answer
Correct answer: Parcel B, by $1 per square foot
A: $120,000 ÷ 20,000 = $6 per square foot. B: $150,000 ÷ 30,000 = $5 per square foot. Difference = $6 − $5 = $1 per square foot, with B lower.
Question 30 of 40
A broker is calculating a commission, a brokerage allocation, and an associate split that produce fractional cents at intermediate steps. When the problem asks for the final payment to the nearest cent and specifies no other rounding rule, what is the best method?
Reveal answer
Correct answer: Retain intermediate precision and round the final payment to cents.
Preserve intermediate precision so successive rounding does not distort the result. Apply the requested cent rounding to the final payment.
Question 31 of 40
An investor's total acquisition and improvement cost is $200,000. Selling expenses will equal 5% of the sale price, with no other costs. What sale price will produce a $28,000 profit after selling expenses?
Reveal answer
Correct answer: $240,000
Required net receipts = $200,000 + $28,000 = $228,000. Seller retains 1 − 0.05 = 0.95 of price. Price = $228,000 ÷ 0.95 = $240,000. Expenses = $240,000 × 0.05 = $12,000; $240,000 − $12,000 − $200,000 = $28,000 profit.
Question 32 of 40
A property cost $160,000. Its owner wants profit equal to 20% of the selling price, with no expenses. What selling price meets that target?
Reveal answer
Correct answer: $200,000
If profit is 20% of price, cost is 100% − 20% = 80% of price. Price = $160,000 ÷ 0.80 = $200,000. Profit = $200,000 − $160,000 = $40,000; $40,000 ÷ $200,000 = 20%.
Question 33 of 40
An investor paid $240,000 for a property, including all acquisition costs. A $275,000 cash offer requires $15,000 in improvements before closing and $22,000 in selling expenses. Which conclusion correctly evaluates the profit?
Reveal answer
Correct answer: The transaction loses $2,000 after all stated costs.
Total stated costs = $240,000 + $15,000 + $22,000 = $277,000. Profit = $275,000 − $277,000 = −$2,000, a $2,000 loss.
Question 34 of 40
A property originally valued at $400,000 declines 20% in value. What percentage increase from the reduced value would restore it to $400,000?
Reveal answer
Correct answer: 25%
Decline = $400,000 × 0.20 = $80,000. Reduced value = $400,000 − $80,000 = $320,000. Required increase = $400,000 − $320,000 = $80,000. Rate = $80,000 ÷ $320,000 = 0.25 = 25%.
Question 35 of 40
A commission is calculated as 3.5% of sales price. Which decimal should be used as the multiplier?
Reveal answer
Correct answer: 0.035
Convert a percentage to a decimal by dividing by 100: 3.5 ÷ 100 = 0.035.
Question 36 of 40
A parcel consists of two adjoining, nonoverlapping rectangles: one is 120 feet by 200 feet and the other is 60 feet by 100 feet. What is the total area?
Reveal answer
Correct answer: 30,000 square feet
First rectangle = 120 × 200 = 24,000 square feet. Second = 60 × 100 = 6,000 square feet. Total = 24,000 + 6,000 = 30,000 square feet.
Question 37 of 40
A brokerage receives 50% of a sale's total commission. Its associate receives 80% of that brokerage share and is paid $8,400. If the total commission was 5% of sales price, what was the sales price?
Reveal answer
Correct answer: $420,000
Brokerage share = $8,400 ÷ 0.80 = $10,500. Total commission = $10,500 ÷ 0.50 = $21,000. Sales price = $21,000 ÷ 0.05 = $420,000.
Question 38 of 40
A lot has 18,000 square feet. Its asking price is $72,000, but the buyer offers $3.60 per square foot. What percentage below the asking price is the offer?
Reveal answer
Correct answer: 10%
Offer = 18,000 × $3.60 = $64,800. Reduction = $72,000 − $64,800 = $7,200. Reduction rate = $7,200 ÷ $72,000 = 0.10 = 10%.
Question 39 of 40
A property costs $200,000. Plan A would sell it for $240,000 with $24,000 in selling expenses. Plan B would sell it for $230,000 with $9,000 in selling expenses. No other costs apply. Which plan yields more profit, and by how much?
Reveal answer
Correct answer: Plan B, by $5,000
A net receipts = $240,000 − $24,000 = $216,000; profit = $216,000 − $200,000 = $16,000. B net receipts = $230,000 − $9,000 = $221,000; profit = $221,000 − $200,000 = $21,000. B exceeds A by $21,000 − $16,000 = $5,000.
Question 40 of 40
An investor buys 2 acres for $100,000 per acre, spends $40,000 on improvements, and sells the entire property for $300,000 with $15,000 in selling expenses. What is the profit percentage on the combined acquisition and improvement cost?
Reveal answer
Correct answer: 18.75%
Acquisition = 2 × $100,000 = $200,000. Combined cost = $200,000 + $40,000 = $240,000. Net sale receipts = $300,000 − $15,000 = $285,000. Profit = $285,000 − $240,000 = $45,000. Rate = $45,000 ÷ $240,000 = 0.1875 = 18.75%.
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