Question 1: If 5 workers can complete a task in 8 hours, how long will 10 workers take to complete the same task? Show your working.

Answer: 4 hours

Question 2: A car consumes 12 liters of fuel to travel 150 km. How much fuel is needed to travel 300 km? Show your working.

Answer: 24 liters

Question 3: A machine's speed is inversely proportional to the time taken to complete a job. If the machine operates at 30 units/hour and takes 4 hours to finish a task, what is its speed if it takes 6 hours? Show your working.

Answer: 20 units/hour

Question 4: Plot the graph of y = 3/x for x values from 1 to 10. Use the grid to draw the curve.

Answer: Curve plotted correctly on grid

Question 5: A worker's efficiency is inversely proportional to the time taken. If a worker takes 5 hours to complete a project, what is the expected time if their efficiency doubles? Show your working.

Answer: 2.5 hours

Question 6: A water tank fills at a rate inversely proportional to the time taken to fill it. If it takes 10 hours to fill the tank at a certain rate, how long will it take if the rate doubles? Show your working.

Answer: 5 hours

Question 7: A car's speed is inversely proportional to the time taken to reach a destination. If the speed is 60 km/h and the time taken is 2 hours, what will be the speed if the time doubles? Show your working.

Answer: 30 km/h

Question 8: A team of workers takes 15 days to complete a project working at a certain rate. If the team size increases to 30 workers, how many days will it take to complete the project? Show your working.

Answer: 7.5 days

Question 9: A recipe requires 4 cups of sugar for 8 servings. If the number of servings is increased to 20, how many cups of sugar are needed? Show your working.

Answer: 10 cups

Question 10: Error Analysis: A student states that if the number of workers doubles, the time taken halves, so the task is completed in 2 hours instead of 4 hours. Identify and explain the mistake.

Answer: The mistake is assuming direct proportion; in inverse proportion, doubling workers halves the time, so it would take 2 hours, which is correct. But if they concluded the time decreases proportionally without considering inverse relation, that would be incorrect.

Question 11: Challenge: A machine's output is inversely proportional to its operating time. If it produces 50 units in 5 hours, how many units will it produce in 8 hours? Show your working.

Answer: 31.25 units

Question 12: Construct a scenario where increasing the number of workers results in a decrease in time, and verify with a calculation that the relation is inverse proportion.

Answer: Example: 3 workers take 12 hours; increasing to 6 workers should reduce time to 6 hours. Calculation: 3 workers * 12 hours = total work; 6 workers * x hours = same work; x = (3*12)/6=6 hours, confirming inverse proportion.