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Solving Proportion Word Problems: Direct and Inverse
Published on April 25, 2026
Word-Problem
This problem set covers direct and inverse proportion word problems, demonstrating how to set up and solve them using ratios and cross-multiplication.
Question
solve these questions
Answer
Here are the solutions to the practice questions provided:
Direct Proportion Questions
Q2. On a recent day, 3 out of 5 stocks in the NYSE declined in price. If 1500 issues were traded, how many declined in price?
- Setup: This is a direct proportion problem. The ratio of declining stocks to total stocks is constant.
- Calculation: Let
be the number of stocks that declined. Multiply both sides by 1500: - Answer: 900 stocks declined in price.
Q3. 50 shares of Titan Corp. stock cost $112.50. How many shares can be bought with $562.50?
- Setup: This is a direct proportion. The cost per share is constant.
- Calculation: Let
be the number of shares that can be bought with $562.50. Cross-multiply: Divide by 112.50: - Answer: 250 shares can be bought.
Q4. You can maintain your body fluid level by drinking four gulps of water every 20 minutes during prolonged exercise. How many gulps do you need for a 2-hour workout?
- Setup: This is a direct proportion. The rate of drinking gulps per minute is constant.
- Calculation:
First, convert 2 hours to minutes:.
The rate is 4 gulps / 20 minutes.
Letbe the number of gulps needed for 120 minutes. - Answer: You need 24 gulps.
Q5. If 5 notebooks cost $200, how much will 8 notebooks cost?
- Setup: This is a direct proportion. The cost per notebook is constant.
- Calculation: Let
be the cost of 8 notebooks. Multiply both sides by 8: - Answer: 8 notebooks will cost $320.
Q6. A car covers 180 km in 3 hours. How far will it travel in 5 hours at the same speed?
- Setup: This is a direct proportion. The speed is constant.
- Calculation: Let
be the distance traveled in 5 hours. Multiply both sides by 5: - Answer: The car will travel 300 km.
Q7. A recipe needs 3 cups of sugar for 12 cupcakes. How much sugar is needed for 20 cupcakes?
- Setup: This is a direct proportion. The amount of sugar per cupcake is constant.
- Calculation: Let
be the amount of sugar needed for 20 cupcakes. Multiply both sides by 20: - Answer: 5 cups of sugar are needed.
Q8. If 6 machines produce 90 units in an hour, how many units will 10 machines produce in the same time?
- Setup: This is a direct proportion. The production rate per machine is constant.
- Calculation: Let
be the number of units produced by 10 machines. Multiply both sides by 10: - Answer: 10 machines will produce 150 units.
Q9. The cost of 7 kg of apples is $630. Find the cost of 5 kg of apples.
- Setup: This is a direct proportion. The cost per kg of apples is constant.
- Calculation: Let
be the cost of 5 kg of apples. Multiply both sides by 5: - Answer: The cost of 5 kg of apples is $450.
Q10. A student reads 30 pages in 50 minutes. How many pages can the student read in 80 minutes at the same rate?
- Setup: This is a direct proportion. The reading rate (pages per minute) is constant.
- Calculation: Let
be the number of pages read in 80 minutes. Multiply both sides by 80: - Answer: The student can read 48 pages.
Q11. A car uses 10 liters of petrol to travel 120 km. How many liters will it use for 300 km?
- Setup: This is a direct proportion. The fuel consumption rate (liters per km) is constant.
- Calculation: Let
be the liters of petrol used for 300 km. Multiply both sides by 300: - Answer: The car will use 25 liters of petrol.
Inverse Proportion Questions
Q12. If 6 men can paint a wall in 9 days, how long will 3 men take to paint the same wall?
- Setup: This is an inverse proportion. The total work (men
days) is constant. - Calculation:
Divide by 3: - Answer: 3 men will take 18 days.
Q13. It takes 12 workers 8 hours to complete a task. How many hours will 16 workers take to complete the same task (assuming equal efficiency)?
- Setup: This is an inverse proportion. The total work (workers
hours) is constant. - Calculation:
Divide by 16: - Answer: 16 workers will take 6 hours.
Q14. A car travels 240 km at 60 km/h. How long will it take to cover the same distance at 80 km/h?
- Setup: This is an inverse proportion. For a fixed distance, speed and time are inversely proportional.
Therefore, . - Calculation:
First, find the time taken at 60 km/h:Now, find the time taken at 80 km/h: Divide by 80: - Answer: It will take 3 hours.
Q15. If 8 typists can type 160 pages in 5 hours, how many typists are needed to type the same number of pages in 2 hours?
- Setup: This is an inverse proportion. The total work (typists
hours) is proportional to the number of pages. For a fixed number of pages, the number of typists and the time taken are inversely proportional. - Calculation:
Divide by 2: - Answer: 20 typists are needed.
Q16. A train travels a fixed distance. If the speed is doubled, how is the time affected?
- Setup: For a fixed distance, speed and time are inversely proportional.
Let the original speed be and the original time be . So, .
The new speed is. Let the new time be . - Calculation:
Since, we can substitute this into the second equation: Divide both sides by : Solve for : - Answer: The time is halved.
Q17. It takes 15 days for 10 men to finish a project. How many men are needed to finish it in 6 days?
- Setup: This is an inverse proportion. The total work (men
days) is constant. - Calculation:
Divide by 6: - Answer: 25 men are needed.
Q18. The pressure of a gas is inversely proportional to its volume. If the pressure is 200 kPa when the volume is 5 L, find the pressure when the volume is 8 L.
- Setup: This is an inverse proportion. Pressure (
) and volume ( ) are inversely proportional, so (constant). - Calculation:
Divide by 8 L: - Answer: The pressure will be 125 kPa.