Ratios, Proportions, Percentages, and Unit Conversions (No Calculator)

Ratios, Proportions, Percentages, and Unit Conversions (No Calculator) – 50 SAT Practice Questions

Ratios, Proportions, Percentages, and Unit Conversions – 50 SAT Practice Questions (No Calculator)

In the SAT Math section – particularly in the domain of Problem Solving and Data Analysis – you will often encounter questions that involve ratios, proportions, percentages, and unit conversions. These concepts are fundamental for interpreting data, solving real-world contexts, and effectively handling quantitative relationships without the aid of a calculator.

This set of 50 practice problems is designed to strengthen your command of these topics. You will see practical applications such as mixing solutions with different concentrations, dealing with scale models, converting between systems of measurement, splitting quantities into ratios, adjusting percentages for taxes or discounts, and more. By studying these problems and understanding the step-by-step solutions, you will not only gain confidence in your arithmetic skills but also develop strategies for translating words into mathematical expressions efficiently—a key skill for the no-calculator portion of the SAT.

As you work through each question, pay special attention to these tips:

Identify the core concept: Is it a ratio question, percentage increase/decrease, or a unit conversion from metric to imperial or vice versa?
Set up equations carefully: Many ratio and proportion problems can be turned into simple equations once you parse the wording accurately.
Convert units systematically: Keep track of what you have (e.g., hours, minutes, miles, kilometers, pounds, kilograms). If needed, always note conversion factors clearly.
Avoid careless mistakes with percentages: Distinguish between “percentage points” changes and “percent changes.” Always confirm whether you’re dealing with a fraction of the original or a fraction of the new total.
Check reasonableness: Always check if your final numeric answer makes sense. Are you expecting a fraction, a whole number, a bigger quantity, or a smaller quantity given the question’s wording?

Below are 50 questions covering a broad range of scenarios, followed by detailed solutions that walk you through every step. These examples will help prepare you to tackle the no-calculator questions confidently and accurately on the SAT. Let’s begin!

Question 1

A recipe for a fruit punch calls for mixing fruit juice and water in a ratio of 3:2 (juice to water). If you want to make 20 cups of this punch, how many cups of fruit juice and how many cups of water should you use?

Solution

The ratio of fruit juice to water is 3:2. This means in every 3 + 2 = 5 parts total, 3 parts are juice and 2 parts are water.

If we need 20 cups of punch, that 20 cups corresponds to 5 parts in total. So each “part” is 20 ÷ 5 = 4 cups.

Therefore, the fruit juice amount is 3 parts × 4 cups/part = 12 cups, and the water amount is 2 parts × 4 cups/part = 8 cups.

Answer: 12 cups of fruit juice and 8 cups of water.

Question 2

The length of a blueprint is drawn at a scale of 1 inch to 4 feet. If the length on the blueprint measures 3.5 inches, how many feet is the actual length?

Solution

The scale is 1 inch : 4 feet. This means 1 inch on the blueprint corresponds to 4 feet in reality. If the blueprint length is 3.5 inches, multiply 3.5 by 4:
3.5 inches × (4 feet / 1 inch) = 14 feet

The actual length is 14 feet.

Question 3

A certain brand of cereal is sold in 800-gram boxes. If a typical portion is 40 grams, how many portions are in each box?

Solution

Each portion is 40 grams, and the box is 800 grams total. Simply divide 800 by 40:
800 ÷ 40 = 20

Thus, one box contains 20 portions.

Question 4

The ratio of the number of students in Club A to the number of students in Club B is 5:7. If there are 20 students in Club A, how many students are in Club B?

Solution

The ratio A:B = 5:7. If A = 20, we set up a proportion:
5 : 7 = 20 : x

Cross-multiply or see that 5 → 20 is a factor of 4, so multiply 7 by 4:
x = 7 × 4 = 28

Hence, Club B has 28 students.

Question 5

A store is offering a 15% discount on an \$80 jacket. How much is the discount, and what is the sale price?

Solution

A 15% discount on \$80 means you reduce the price by 15% of \$80.
15% of 80 = 0.15 × 80 = \$12

So the discount is \$12, and the sale price is 80 - 12 = \$68.

Answer: Discount = \$12, Sale price = \$68.

Question 6

After receiving a 10% raise, Jessica’s salary is \$66,000. What was her salary before the raise?

Solution

A 10% raise means the new salary is 110% (or 1.10 times) of the old salary. Let S be the old salary. Then:
1.10 × S = 66,000
S = 66,000 ÷ 1.10 = 60,000

Jessica’s old salary was \$60,000.

Question 7

A medical solution is labeled 25 mg of medication per 2 mL of solution. How many mg of medication are in 10 mL of solution at the same concentration?

Solution

The ratio is 25 mg medication : 2 mL solution. We want to find how many mg in 10 mL. Let x = mg in 10 mL:
25 mg / 2 mL = x mg / 10 mL

Cross-multiply:
25 × 10 = 2x
250 = 2x
x = 125

There are 125 mg of medication in 10 mL of solution.

Question 8

A map uses a scale of 1:100,000 (1 cm represents 100,000 cm in reality). If two cities are 3.2 cm apart on the map, how many kilometers apart are they in reality? (Note: 100 cm = 1 m, 1000 m = 1 km.)

Solution

A scale of 1:100,000 means 1 cm on the map equals 100,000 cm in actual distance. If the distance on the map is 3.2 cm, the real distance in centimeters is:
3.2 × 100,000 = 320,000 cm

Now convert centimeters to kilometers. First, convert cm to meters:
320,000 cm ÷ 100 = 3,200 m

Then convert meters to kilometers:
3,200 m ÷ 1000 = 3.2 km

So the two cities are 3.2 kilometers apart in reality.

Question 9

A container is labeled in quarts, and another container is labeled in liters. We know 1 quart ≈ 0.95 liters. If the quart container holds 10 quarts of water, how many liters does it hold, approximately?

Solution

Given 1 quart ≈ 0.95 liters, for 10 quarts:
10 quarts × 0.95 liters/quart = 9.5 liters

So the container holds about 9.5 liters.

Question 10

A certain brand of socks sells 3 pairs for \$8. If you want to buy 12 pairs, how much will it cost assuming the same rate?

Solution

3 pairs cost \$8, so 1 pair costs \$8 ÷ 3 = \$2.67 approximately. For 12 pairs:
12 × (8 ÷ 3) = 12 × 2.666... = \$32

Alternatively, note that 12 pairs is 4 times 3 pairs, so 4 × 8 = \$32.

The cost for 12 pairs is \$32.

Question 11

The ratio of a rectangle’s length to its width is 5:3. If the width is 15 cm, what is the length?

Solution

The ratio length:width = 5:3. Let length = 5k, width = 3k. Since width is 15 cm, that means 3k = 15 → k = 5.

Then length = 5k = 5 × 5 = 25 cm.

The length is 25 cm.

Question 12

A solution contains 40% sugar. If you have 250 grams of this solution, how many grams of sugar does it contain?

Solution

If the solution is 40% sugar, then in 250 grams, the sugar mass is 0.40 × 250 = 100 grams.

So it contains 100 grams of sugar.

Question 13

A discount store reduces the price of all electronics by 25%. If the original price of a television is \$400, what is the discounted price?

Solution

25% off \$400 is 0.25 × 400 = \$100 discount. Hence, the sale price is 400 - 100 = \$300.

Answer: \$300.

Question 14

The price of a gallon of milk increases from \$2.80 to \$3.00. What is the percentage increase?

Solution

The increase in price is 3.00 - 2.80 = \$0.20. To find the percentage increase, compare to the original \$2.80:
(0.20 ÷ 2.80) × 100% = (0.20 / 2.80) × 100% = 1/14 × 100% ≈ 7.14%

The price increases by about 7.14%.

Question 15

A car travels 100 miles using 4 gallons of gas. At this rate, how many miles can it travel using 10 gallons of gas?

Solution

The car’s mileage is 100 miles per 4 gallons, i.e., 25 miles/gallon. For 10 gallons:
25 miles/gallon × 10 gallons = 250 miles

The car can travel 250 miles with 10 gallons.

Question 16

The ratio of boys to girls in a classroom is 2:3. If there are 18 girls, how many boys are in the classroom?

Solution

B:G = 2:3. If G = 18, we see how 3 scales to 18: that’s a factor of 6. Multiply 2 by 6 for the boys:
2 × 6 = 12

There are 12 boys in the classroom.

Question 17

A jar of peanut butter is labeled 16 ounces (oz). If 1 pound (lb) equals 16 ounces, how many jars are needed to have 5 pounds of peanut butter?

Solution

1 jar = 16 oz = 1 lb. To have 5 lb, you need 5 jars.

So, 5 jars are required.

Question 18

Samantha’s weekly paycheck is 15% more than Rebecca’s. If Rebecca earns \$520, how much does Samantha earn?

Solution

Samantha’s pay is 15% more than \$520, i.e., 520 + 0.15 × 520 = 520 + 78 = \$598.

Samantha earns \$598.

Question 19

A car’s value depreciates by 20% from its initial \$25,000 purchase price in the first year. What is the value after one year?

Solution

20% of 25,000 = 0.20 × 25,000 = \$5,000. So the new value is 25,000 - 5,000 = \$20,000.

Value after one year is \$20,000.

Question 20

A pipe delivers water at a rate of 3 gallons per minute. How many gallons of water are delivered in half an hour?

Solution

Half an hour is 30 minutes. At 3 gallons/min, in 30 minutes:
3 × 30 = 90 gallons

The pipe delivers 90 gallons in half an hour.

Question 21

A 12-ounce can of soda costs \$0.60. Assuming a direct proportion, how much would a 20-ounce bottle of the same soda cost?

Solution

We have 12 ounces → \$0.60. If we let x = cost for 20 oz:
0.60 / 12 = x / 20

Cross-multiply:
0.60 × 20 = 12x
12 = 12x
x = 1

So a 20-ounce bottle would cost \$1.00, assuming the same rate per ounce.

Question 22

You drive 270 miles on 9 gallons of gas. What is your car’s fuel efficiency in miles per gallon (mpg)?

Solution

The efficiency is distance ÷ gallons:
270 ÷ 9 = 30 mpg

The car’s efficiency is 30 mpg.

Question 23

If 1 inch is 2.54 centimeters, how many centimeters are in 5 inches?

Solution

1 inch = 2.54 cm. Then 5 inches = 5 × 2.54 = 12.7 cm.

So 5 inches is 12.7 cm.

Question 24

A real estate agent earns 3% commission on a house she sells. If she earns \$9,000 in commission, what was the selling price of the house?

Solution

3% of the selling price = \$9,000. Let P = selling price:
0.03P = 9,000
P = 9,000 ÷ 0.03 = 300,000

The house sold for \$300,000.

Question 25

A car travels 60 miles in 1 hour 20 minutes. Express its speed in miles per hour as a fraction or mixed number.

Solution

1 hour 20 minutes is 1⅓ hours (or 1.333... hours). Speed = distance ÷ time = 60 ÷ (4/3) = 60 × (3/4) = 45 mph.

Alternatively, 1 hour 20 min = 80 minutes, so speed in mph:
Speed = 60 miles / (80/60 hours) = 60 / (4/3) = 45 mph.

Answer: 45 mph.

Question 26

In a certain college, the ratio of graduate students to undergraduate students is 2:5. If there are 3,000 graduate students, how many undergraduate students are there?

Solution

The ratio G:U = 2:5. If G = 3,000, observe how 2 corresponds to 3,000. That’s a factor of 1,500. Multiply 5 by 1,500 to find the undergrads:
5 × 1,500 = 7,500

So, 7,500 undergraduates.

Question 27

A container is labeled “1 gallon.” We know 1 gallon is about 3.8 liters. If you have 2 gallons of water, how many liters is that approximately?

Solution

If 1 gallon ≈ 3.8 liters, then 2 gallons ≈ 2 × 3.8 = 7.6 liters.

Answer: 7.6 liters (approximately).

Question 28

A clothing store marks down all items by 25%. If an item’s original price is \$84, what is its sale price after this markdown?

Solution

25% of 84 = 0.25 × 84 = 21. So the item is discounted by \$21, and the sale price is 84 - 21 = \$63.

Answer: \$63.

Question 29

The price of a phone decreases from \$400 to \$320. What is the percent decrease?

Solution

The decrease is 400 - 320 = \$80. Compare to the original \$400:
(80 ÷ 400) × 100% = 0.20 × 100% = 20%

The percent decrease is 20%.

Question 30

A medication instruction says to administer 2 mL for every 10 kilograms of a patient’s body weight. If a patient weighs 65 kilograms, how many mL should be administered?

Solution

The ratio is 2 mL : 10 kg. Let x = mL for 65 kg:
2 / 10 = x / 65

Cross-multiply:
2 × 65 = 10x
130 = 10x
x = 13

The dosage is 13 mL.

Question 31

A machine can produce 50 widgets in 15 minutes. At the same rate, how many widgets can it produce in 1 hour?

Solution

1 hour is 60 minutes. The rate is 50 widgets/15 min. We want widgets in 60 min:
In 15 minutes → 50 widgets
In 60 minutes (which is 4 times 15) → 50 × 4 = 200 widgets

The machine produces 200 widgets in 1 hour.

Question 32

The ratio of red marbles to blue marbles in a bag is 7:9. If there are 63 red marbles, how many blue marbles are there?

Solution

R:B = 7:9. If R = 63, that’s 7 times 9. The scale factor is 63 ÷ 7 = 9. Multiply 9 × 9 = 81 for blue marbles.

81 blue marbles.

Question 33

A sample of 200 voters shows that 40% plan to vote for Candidate A. If this ratio holds for the entire population of 10,000 voters, how many are predicted to vote for Candidate A?

Solution

40% of 10,000 = 0.40 × 10,000 = 4,000.

Predicted number of votes for Candidate A is 4,000.

Question 34

A discount coupon takes \$5 off a purchase, and then an additional 20% off the reduced price. If the original price is \$50, what is the final amount paid?

Solution

First, subtract \$5 from \$50 → \$45. Then take 20% off \$45 → 20% of 45 = 9. So the discount is \$9, leaving 45 - 9 = \$36.

The final amount is \$36.

Question 35

The population of a city increases from 80,000 to 92,000 in one year. What is the percent increase to the nearest tenth?

Solution

The increase is 92,000 - 80,000 = 12,000. We compare to the original 80,000:
(12,000 ÷ 80,000) × 100% = 0.15 × 100% = 15%

So the increase is exactly 15%. To the nearest tenth, that remains 15.0%.

Question 36

A construction worker needs 8 nails per foot of wooden beam. If there are 36 feet of beam to secure, how many nails are required in total?

Solution

8 nails/foot × 36 feet = 288 nails

The worker needs 288 nails total.

Question 37

The exchange rate is \$1 = 0.90 euros. If a traveler exchanges \$200, how many euros does he receive (before any fees)?

Solution

1 dollar → 0.90 euros. So 200 dollars → 200 × 0.90 = 180 euros.

He receives 180 euros.

Question 38

The ratio of the weight of a metal bar in kilograms to pounds is about 1:2.2. If a bar weighs 44 pounds, approximately how many kilograms does it weigh?

Solution

The ratio kg:lb = 1:2.2. If the bar weighs 44 lb, we have 2.2 → 1 in ratio form. Let x = kg:
x / 44 = 1 / 2.2

So x = 44 × (1/2.2) = 44 / 2.2 = 20

The bar weighs about 20 kilograms.

Question 39

A doughnut shop sells 5 doughnuts for \$4. If Megan buys 15 doughnuts at the same rate, how much does she pay?

Solution

5 doughnuts cost \$4, so 1 doughnut costs \$4 ÷ 5 = \$0.80. For 15 doughnuts: 15 × 0.80 = \$12.

Alternatively, 15 is 3 sets of 5, so 3 × \$4 = \$12.

Megan pays \$12.

Question 40

A baby weighs 3.2 kilograms at birth. If 1 kilogram is about 2.2 pounds, how many pounds does the baby weigh, approximately?

Solution

Convert kg to lb by multiplying by 2.2:
3.2 × 2.2 = 7.04

The baby weighs about 7.04 pounds, typically rounded to 7.0 lbs or about 7 lbs.

Question 41

A store marks up every item by 20% of its cost. If an item costs \$50 for the store to buy, what is the selling price to customers?

Solution

20% of 50 = 0.20 × 50 = \$10. So the store sells it for 50 + 10 = \$60.

The selling price is \$60.

Question 42

A 2-liter bottle of juice costs \$3. A 3-liter bottle of the same juice costs \$4.50. If the price per liter is the same for both, which is the better deal?

Solution

Compute price per liter for the 2-liter bottle: \$3 ÷ 2 L = \$1.50 per liter.

For the 3-liter bottle: \$4.50 ÷ 3 L = \$1.50 per liter.

The cost per liter is the same (\$1.50 per liter) for both.

Answer: They cost the same per liter.

Question 43

A mixture is 30% oil by volume. If you have 200 mL of this mixture, how many mL of oil does it contain?

Solution

30% of 200 mL = 0.30 × 200 = 60 mL.

It contains 60 mL of oil.

Question 44

A man weighs 220 pounds. If 1 pound is 0.45 kilograms, how many kilograms does he weigh (approx.)?

Solution

Multiply 220 by 0.45:
220 × 0.45 = 99

He weighs about 99 kilograms.

Question 45

A jar contains green and yellow jellybeans in a ratio 3:5. If there are 240 yellow jellybeans, how many green jellybeans are there?

Solution

G:Y = 3:5. If Y = 240, we see 5 corresponds to 240, factor is 240 ÷ 5 = 48. Multiply 3 by 48 to find green jellybeans:
3 × 48 = 144

There are 144 green jellybeans.

Question 46

A computer is on sale for 30% off. If its original price is \$1,000, and there is also a sales tax of 8% on the discounted price, how much do you pay in total?

Solution

First, 30% off \$1,000 is a \$300 discount, so discounted price = \$700. Then we have 8% sales tax on \$700:
0.08 × 700 = \$56

So the total is 700 + 56 = \$756.

The final price is \$756.

Question 47

In a poll, 45 out of 100 surveyed said they prefer brand X cereal. If the city has 10,000 people, how many can we predict prefer brand X, based on this sample proportion?

Solution

45 out of 100 is 45%. Of 10,000, 45% is 0.45 × 10,000 = 4,500.

So we predict 4,500 people prefer brand X.

Question 48

A sign says 1 mile = 1.6 kilometers. How many kilometers are in 5 miles?

Solution

Multiply 5 by 1.6:
5 × 1.6 = 8

5 miles is 8 kilometers.

Question 49

After getting a 25% discount, a pair of shoes costs \$45. What was the original price of the shoes before the discount?

Solution

If there is a 25% discount, the shoes are purchased at 75% of the original price. Let P = original price:
0.75P = 45
P = 45 ÷ 0.75 = 60

The original price was \$60.

Question 50

A 6-pack of juice boxes costs \$4.80. At the same rate, how much would a 10-pack of juice boxes cost?

Solution

6-pack cost \$4.80, so price per box is 4.80 ÷ 6 = \$0.80. For 10 boxes:
10 × 0.80 = \$8.00

A 10-pack would cost \$8.00.

Conclusion and Final Tips

You have now worked through 50 detailed practice questions on ratios, proportions, percentages, and unit conversions, all of which can appear in the SAT’s Problem Solving and Data Analysis domain. Here are a few final tips to reinforce your test-taking strategy:

Re-check units: Always verify that your units match what the problem asks for. Converting from one system to another (e.g., inches to centimeters, pounds to kilograms) is a frequent source of error.
Practice mental arithmetic: Because this is the no-calculator portion, get comfortable with fractional manipulations and basic multiplication/division in your head.
Identify the “original value” in percentage problems: Many mistakes arise from mixing up what is the reference value for the percentage increase or decrease.
Draw quick sketches for ratio or scale scenarios: For example, if a map question says 1 inch : 5 miles, it might help to visualize or set up a proportion to solve for the unknown real distance.
Double-check reasonableness: If you get a 200% discount or a negative price, something’s amiss. Use a quick logic check to ensure your final answer is realistic.

Consistent practice with these topics will sharpen your problem-solving skills and boost your confidence. Keep refining your approach, and best of luck as you tackle the SAT Math section!