ACCUPLACER Quantitative Reasoning, Algebra & Statistics Quiz: Ratio And Rate Problems
20 questions · exam conditions
0:00
Ratio And Rate ProblemsQuestion 1 of 20

A cyclist travels at an average speed of 18 kilometers per hour. How many meters does the cyclist travel in 20 minutes? (1 kilometer = 1000 meters)

360
5,400
6,000
18,000
← Back to quizzes

ACCUPLACER Quantitative Reasoning, Algebra & Statistics Quiz

ACCUPLACER Quantitative Reasoning, Algebra & Statistics Quiz: Ratio And Rate Problems

Practice Ratio And Rate Problems in ACCUPLACER Quantitative Reasoning, Algebra & Statistics with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Ratio And Rate Problems, giving you a quick way to practice the rules, question types, and explanations that matter most for ACCUPLACER Quantitative Reasoning, Algebra & Statistics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A cyclist travels at an average speed of 18 kilometers per hour. How many meters does the cyclist travel in 20 minutes? (1 kilometer = 1000 meters)

  1. 360
  2. 5,400
  3. 6,000 (correct answer)
  4. 18,000
Explanation: First, convert the speed to meters per minute. Speed is 18kmhr×1000mkm=18,000mhr18 \frac{\text{km}}{\text{hr}} \times 1000 \frac{\text{m}}{\text{km}} = 18,000 \frac{\text{m}}{\text{hr}}. Then convert hours to minutes: 18,000mhr÷60minhr=300mmin18,000 \frac{\text{m}}{\text{hr}} \div 60 \frac{\text{min}}{\text{hr}} = 300 \frac{\text{m}}{\text{min}}. Finally, multiply the rate by the time in minutes: 300mmin×20 min=6,000300 \frac{\text{m}}{\text{min}} \times 20 \text{ min} = 6,000 meters.

Question 2

The ratio of the length to the width of a rectangle is 7:4. If the perimeter of the rectangle is 88 centimeters, what is the width of the rectangle?

  1. 4 cm
  2. 16 cm (correct answer)
  3. 22 cm
  4. 28 cm
Explanation: Let the length be 7x7x and the width be 4x4x. The perimeter is given by P=2(l+w)P = 2(l + w). Substitute the given values: 88=2(7x+4x)88 = 2(7x + 4x). This simplifies to 88=2(11x)88 = 2(11x), or 88=22x88 = 22x. Solving for xx gives x=4x = 4. The question asks for the width, which is 4x4x. So, the width is 4×4=164 \times 4 = 16 cm.

Question 3

A recipe for 18 cookies requires 2.25 cups of flour. A baker needs to make exactly 30 cookies. Based on the recipe's ratio, how many cups of flour are needed?

  1. 1.35
  2. 3.45
  3. 3.75 (correct answer)
  4. 4.05
Explanation: First, find the amount of flour required per cookie: 2.25 cups÷18 cookies=0.1252.25 \text{ cups} \div 18 \text{ cookies} = 0.125 cups per cookie. Then, multiply this unit rate by the desired number of cookies: 0.125cupscookie×30 cookies=3.750.125 \frac{\text{cups}}{\text{cookie}} \times 30 \text{ cookies} = 3.75 cups.

Question 4

A cleaning solution is made by mixing concentrate with water in a ratio of 1 to 8. If a bottle contains 540 milliliters of the final cleaning solution, how many milliliters of concentrate were used?

  1. 60 (correct answer)
  2. 67.5
  3. 72
  4. 480
Explanation: The ratio of concentrate to water is 1:8, which means there are 1+8=91 + 8 = 9 total parts in the solution. The total volume is 540 ml. To find the volume of one part, divide the total volume by the total number of parts: 540 ml÷9 parts=60mlpart540 \text{ ml} \div 9 \text{ parts} = 60 \frac{\text{ml}}{\text{part}}. Since the concentrate is 1 part, 60 ml of concentrate were used.

Question 5

A chemist has a 20-liter solution that is 15% acid. How many liters of pure water must be added to the solution to dilute it to a concentration of exactly 10% acid?

  1. 1
  2. 5
  3. 10 (correct answer)
  4. 15
Explanation: First, find the amount of acid, which remains constant: 20 L×0.15=320 \text{ L} \times 0.15 = 3 liters of acid. Let WW be the liters of water added. The new total volume will be 20+W20 + W. The new concentration equation is 320+W=0.10\frac{3}{20 + W} = 0.10. To solve for WW, multiply both sides by 20+W20 + W to get 3=0.10(20+W)3 = 0.10(20 + W). This simplifies to 3=2+0.1W3 = 2 + 0.1W. Subtracting 2 from both sides gives 1=0.1W1 = 0.1W. Dividing by 0.1 gives W=10W = 10 liters.

Question 6

A currency exchange service converts U.S. dollars (USD) to euros (EUR) at a rate of 1 USD = 0.92 EUR. The service charges a 3% fee on the initial USD amount before making the exchange. How many euros would a customer receive for exchanging $500 USD?

  1. 446.20446.20 (correct answer)
  2. 460.00460.00
  3. 473.80473.80
  4. 475.00475.00
Explanation: First, calculate the 3% fee on the USD amount: (500 \times 0.03 = 15\). Subtract the fee from the initial amount: \(500 - 15=15 = 485). Finally, convert the remaining USD to EUR: ($485 \times 0.92 = 446.20) EUR.

Question 7

Car A has a fuel efficiency of 25 miles per gallon. Car B is advertised as having a fuel efficiency that is 30% greater than Car A's. For a 650-mile trip, how many fewer gallons of fuel does Car B use compared to Car A?

  1. 6.0 (correct answer)
  2. 7.5
  3. 7.8
  4. 20.0
Explanation: First, calculate Car B's fuel efficiency: 25 mpg×1.30=32.525 \text{ mpg} \times 1.30 = 32.5 mpg. Next, calculate the gallons used by each car for the trip. Car A uses 650÷25=26650 \div 25 = 26 gallons. Car B uses 650÷32.5=20650 \div 32.5 = 20 gallons. The difference is 26−20=626 - 20 = 6 gallons.

Question 8

On a regional map, the scale is 1.5 inches to 40 miles. If the distance between two cities on the map is 10.5 inches, what is the actual distance between the cities?

  1. 240 miles
  2. 280 miles (correct answer)
  3. 315 miles
  4. 630 miles
Explanation: Set up a proportion to solve for the actual distance, xx: 1.5 inches40 miles=10.5 inchesx miles\frac{1.5 \text{ inches}}{40 \text{ miles}} = \frac{10.5 \text{ inches}}{x \text{ miles}}. Cross-multiply to get 1.5x=40×10.51.5x = 40 \times 10.5, which simplifies to 1.5x=4201.5x = 420. Divide by 1.5 to find x=280x = 280 miles.

Question 9

The ratio of apples to oranges in a fruit basket is initially 5:3. After 4 apples are removed and 4 oranges are added, the ratio of apples to oranges becomes 1:1. How many apples were in the basket originally?

  1. 4
  2. 12
  3. 16
  4. 20 (correct answer)
Explanation: Let the original number of apples be 5x5x and oranges be 3x3x. After the change, the number of apples is 5x−45x - 4 and the number of oranges is 3x+43x + 4. The new ratio is 1:1, so 5x−4=3x+45x - 4 = 3x + 4. To solve for xx, subtract 3x3x from both sides to get 2x−4=42x - 4 = 4. Add 4 to both sides to get 2x=82x = 8, which means x=4x = 4. The original number of apples was 5x5x, so 5×4=205 \times 4 = 20.

Question 10

A store sells a pack of 8 batteries for $7.60. A different store sells a pack of 12 of the same brand of batteries for $10.80. What is the positive difference in the price per battery between the two stores?

  1. $0.05 (correct answer)
  2. $0.32
  3. $0.80
  4. $0.92
Explanation: First, find the unit price for the first store: (7.60÷8=7.60 \div 8 = 0.95) per battery. Next, find the unit price for the second store: (10.80÷12=10.80 \div 12 = 0.90) per battery. The difference in price per battery is (0.95−0.95 - 0.90 = $0.05).

Question 11

In a mechanical system, a small gear with 12 teeth is interlocked with a large gear with 30 teeth. For every 5 complete rotations of the small gear, how many complete rotations does the large gear make?

  1. 2 (correct answer)
  2. 3
  3. 7.5
  4. 12.5
Explanation: The number of teeth moved by the small gear is 5 rotations×12 teeth/rotation=605 \text{ rotations} \times 12 \text{ teeth/rotation} = 60 teeth. The large gear must also move by 60 teeth. To find the number of rotations for the large gear, divide the total teeth moved by the number of teeth on the large gear: 60 teeth÷30 teeth/rotation=260 \text{ teeth} \div 30 \text{ teeth/rotation} = 2 rotations.

Question 12

An internet company charges $30 per month for the first 100 gigabytes (GB) of data. For every gigabyte over 100, the company charges an additional $0.75. If a customer's bill for one month was $48.75, how many total gigabytes of data did they use?

  1. 25
  2. 65
  3. 125 (correct answer)
  4. 165
Explanation: First, find the portion of the bill that is for data overage: (48.75−48.75 - 30.00 = 18.75\). Next, determine how many gigabytes of overage this amount represents by dividing by the per-gigabyte rate: \(18.75 \div 0.75/\text{GB} = 25\) GB. This is the amount of data used *over* the initial 100 GB. The total data used is the initial allotment plus the overage: 100 \text{ GB} + 25 \text{ GB} = 125$ GB.

Question 13

A printer has a constant rate of 12 pages per minute. The printer is scheduled to run for a 2.5-hour period, but it is idle for a total of 30 minutes for paper refills during that time. How many pages are printed in total?

  1. 1,080
  2. 1,440 (correct answer)
  3. 1,794
  4. 1,800
Explanation: First, convert the total scheduled time to minutes: 2.5 hours×60minuteshour=1502.5 \text{ hours} \times 60 \frac{\text{minutes}}{\text{hour}} = 150 minutes. Subtract the idle time to find the active printing time: 150 minutes−30 minutes=120150 \text{ minutes} - 30 \text{ minutes} = 120 minutes. Finally, multiply the active time by the printing rate: 120 minutes×12pagesminute=1,440120 \text{ minutes} \times 12 \frac{\text{pages}}{\text{minute}} = 1,440 pages.

Question 14

A farmer can harvest a field of corn in 10 hours using a combine. An assistant can harvest the same field in 15 hours using a smaller machine. If the farmer works alone for 4 hours and then the assistant joins to finish the harvest, how many hours will it take for them to finish the remaining work together?

  1. 2.4
  2. 3.6 (correct answer)
  3. 4.0
  4. 6.0
Explanation: The farmer's rate is 110\frac{1}{10} field/hour. The assistant's rate is 115\frac{1}{15} field/hour. In 4 hours, the farmer completes 4×110=410=254 \times \frac{1}{10} = \frac{4}{10} = \frac{2}{5} of the field. The remaining work is 1−25=351 - \frac{2}{5} = \frac{3}{5} of the field. Their combined rate is 110+115=330+230=530=16\frac{1}{10} + \frac{1}{15} = \frac{3}{30} + \frac{2}{30} = \frac{5}{30} = \frac{1}{6} field/hour. Time to finish is Work÷Rate=3/51/6=35×6=185=3.6\text{Work} \div \text{Rate} = \frac{3/5}{1/6} = \frac{3}{5} \times 6 = \frac{18}{5} = 3.6 hours.

Question 15

Object A has a mass of 450 grams and a volume of 75 cubic centimeters. Object B has a density that is 20% greater than Object A. If Object B has a mass of 360 grams, what is its volume in cubic centimeters? (Density = Mass / Volume)

  1. 48
  2. 50 (correct answer)
  3. 60
  4. 72
Explanation: First, calculate the density of Object A: DensityA=450 g75 cm3=6gcm3\text{Density}_A = \frac{450 \text{ g}}{75 \text{ cm}^3} = 6 \frac{\text{g}}{\text{cm}^3}. Next, calculate the density of Object B, which is 20% greater: DensityB=6×1.20=7.2gcm3\text{Density}_B = 6 \times 1.20 = 7.2 \frac{\text{g}}{\text{cm}^3}. Finally, use the density formula to find the volume of Object B: VolumeB=MassBDensityB=360 g7.2 g/cm3=50 cm3\text{Volume}_B = \frac{\text{Mass}_B}{\text{Density}_B} = \frac{360 \text{ g}}{7.2 \text{ g/cm}^3} = 50 \text{ cm}^3.

Question 16

A town's population grew from 12,500 to 13,000 in one year. If the population continues to grow at this same annual rate, what will the population be after two more years, starting from 13,000? (Round to the nearest whole number)

  1. 13,520
  2. 14,000
  3. 14,040
  4. 14,061 (correct answer)
Explanation: First, find the rate of growth. The increase was 13,000−12,500=50013,000 - 12,500 = 500. The rate is 50012,500=0.04\frac{500}{12,500} = 0.04, or 4% per year. This means each year the population is multiplied by 1.04. After one more year: 13,000×1.04=13,52013,000 \times 1.04 = 13,520. After the second year: 13,520×1.04=14,060.813,520 \times 1.04 = 14,060.8. Rounded to the nearest whole number, the population is 14,061.

Question 17

In a school, the ratio of teachers to students is 1:24. If there are 18 teachers, and the school wants to reduce this ratio to 1:20, how many students must transfer to other schools?

  1. 78 students
  2. 72 students (correct answer)
  3. 84 students
  4. 96 students
Explanation: When you encounter ratio problems involving changes, you need to work systematically through the current situation, the desired situation, and find the difference. First, find the current number of students. With 18 teachers and a 1:24 ratio, you have 18×24=43218 \times 24 = 432 students currently. Next, determine how many students the school should have with the new 1:20 ratio. With the same 18 teachers, the new target is 18×20=36018 \times 20 = 360 students. The difference tells you how many students must transfer: 432−360=72432 - 360 = 72 students need to leave, making B correct. Looking at the wrong answers: A) 78 students represents a calculation error, possibly from incorrectly computing 18×24−18×2018 \times 24 - 18 \times 20 as 18×(24−20)+618 \times (24-20) + 6. C) 84 students might come from miscalculating one of the products, perhaps getting 18×24=44418 \times 24 = 444 instead of 432. D) 96 students could result from finding 18×(24−20)=18×4=7218 \times (24-20) = 18 \times 4 = 72, then accidentally adding 24 to get 96. For ratio change problems, always follow this three-step approach: calculate the current total using the given ratio, calculate the target total using the new ratio, then find the difference. Don't try to work directly with the ratio difference—that's a common trap that leads to incorrect answers.

Question 18

A construction crew can build 150 feet of fence in 4 hours when working at full capacity. Today, only 75% of the crew is available, and they work for 6 hours. How many feet of fence will they complete?

  1. 225 feet
  2. 180 feet
  3. 202.5 feet
  4. 168.75 feet (correct answer)
Explanation: When you encounter work rate problems, you need to establish the baseline rate first, then adjust for changes in workforce and time. This question tests your ability to handle proportional reasoning with multiple variables. Start by finding the crew's rate at full capacity: 150 feet4 hours=37.5 feet per hour\frac{150 \text{ feet}}{4 \text{ hours}} = 37.5 \text{ feet per hour}. This tells you what the complete crew can accomplish in one hour. Today, only 75% of the crew is available, so their rate becomes: 37.5×0.75=28.125 feet per hour37.5 \times 0.75 = 28.125 \text{ feet per hour}. Working for 6 hours at this reduced rate gives you: 28.125×6=168.75 feet28.125 \times 6 = 168.75 \text{ feet}. Choice A (225 feet) assumes the reduced crew somehow works faster than the full crew — this would require them to build at 37.5 feet per hour despite being understaffed. Choice B (180 feet) correctly calculates the 75% workforce reduction but mistakenly uses the original 4-hour timeframe instead of 6 hours. Choice C (202.5 feet) represents what would happen if you took 75% of what the full crew could do in 6 hours (270 feet × 0.75), but this incorrectly assumes the full crew's rate scales linearly to 6 hours before applying the reduction. The correct answer is D (168.75 feet). Remember: In work rate problems, always calculate the rate per unit time first, apply any workforce changes to that rate, then multiply by the actual time worked. Don't mix up the order of operations.

Question 19

A printer can print 180 pages in 15 minutes. After printing for 25 minutes at this rate, the printer's speed decreases by 20%. How many additional minutes will it take to print 60 more pages at the reduced speed?

  1. 10.0 minutes
  2. 7.5 minutes
  3. 8.0 minutes
  4. 6.25 minutes (correct answer)
Explanation: When you encounter multi-step rate problems like this, break them down into clear phases and track how conditions change between phases. First, find the printer's initial rate: 180 pages15 minutes=12 pages per minute\frac{180 \text{ pages}}{15 \text{ minutes}} = 12 \text{ pages per minute} The question asks about printing 60 additional pages after the speed decreases by 20%. When speed decreases by 20%, the new speed is 80% of the original: 12×0.8=9.6 pages per minute12 \times 0.8 = 9.6 \text{ pages per minute} To find the time needed for 60 pages at this reduced speed: 60 pages9.6 pages per minute=6.25 minutes\frac{60 \text{ pages}}{9.6 \text{ pages per minute}} = 6.25 \text{ minutes} This confirms answer D) 6.25 minutes is correct. The wrong answers reflect common calculation errors: A) 10.0 minutes likely comes from incorrectly using 6 pages per minute (half the original rate instead of 80%). B) 7.5 minutes results from using 8 pages per minute, possibly from rounding 9.6 down carelessly. C) 8.0 minutes comes from using 7.5 pages per minute, which might result from confusing the percentage decrease or making arithmetic errors in the rate calculation. Strategy tip: In multi-step rate problems, always verify your rate calculations before moving to the final step. Write down each rate clearly (original rate, then modified rate) and double-check your percentage calculations. The phrase "decreased by 20%" means multiply by 0.8, not 0.2.

Question 20

A car travels 285 miles and uses 12 gallons of gasoline. At this rate, how many miles can the car travel on a full tank of 16.5 gallons?

  1. 392.5 miles (correct answer)
  2. 396.25 miles
  3. 412.5 miles
  4. 427.5 miles
Explanation: First find the rate: 285 miles ÷ 12 gallons = 23.75 miles per gallon. Then multiply by the full tank: 23.75 × 16.5 = 392.5 miles. Choice B uses an incorrect calculation of the rate (285 ÷ 12 = 24). Choice C adds the additional 4.5 gallons to the original distance incorrectly. Choice D assumes a round number rate of 25 mpg.