Inverse Proportion and Work Problems

The video tutorial explains inverse proportion through various examples, including workers, machines, and taps. It highlights common misconceptions and emphasizes logical reasoning. The tutorial also covers complex problems involving varying numbers of workers and machines over different days. The video concludes with a preview of the next topic on algebraic forms of direct and inverse proportion.

What is inverse proportion?

• A relationship where one quantity increases as another increases.

• A relationship where one quantity decreases as another increases.

• A relationship where both quantities remain constant.

• A relationship where both quantities increase together.

If 10 workers take 4 days to complete a job, how long will 8 workers take?

• 7 days

• 6 days

• 5 days

• 3 days

How do you calculate the time taken by one worker if 10 workers take 4 days?

• Multiply 4 by 10

• Add 10 and 4

• Multiply 10 by 4

• Divide 4 by 10

If 8 machines take 6 days to complete a job, how long will 12 machines take?

• 3 days

• 4 days

• 6 days

• 5 days

What is the first step in solving an inverse proportion problem involving machines?

• Calculate the time for one machine.

• Calculate the time for double the machines.

• Calculate the time for two machines.

• Calculate the time for half the machines.

If 6 taps take 12 hours to fill a tank, how long will 8 taps take?

• 11 hours

• 10 hours

• 9 hours

• 8 hours

What assumption is made about the taps in the inverse proportion problem?

• All taps have different flow rates.

• All taps have the same flow rate.

• Some taps are faster than others.

• Some taps are slower than others.

In a practice problem, if 4 workers take 9 days, how long will 3 workers take?

• 10 days

• 13 days

• 11 days

• 12 days

If 5 taps take 16 hours, how long will 8 taps take?

• 8 hours

• 10 hours

• 12 hours

• 14 hours

In a complex problem, if 8 machines take 9 days, how many days will it take if the number of machines varies each day?

• 13 days

• 12 days

• 11 days

• 10 days