Percentages and ratio · Ages 13–14

Inverse proportion worksheet

Part of: Rates, ratios & proportions

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Percentages and ratio · Ages 13–14

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.y is in inverse proportion to x, and y = 2 when x = 3. In xy = k, k = ; when x = 2, y = .
Fill in each blank
Answer:
2.8 people take 3 days over a job. Working as fast, 4 people take days
Answer:
3.y is in inverse proportion to x, and y = 3 when x = 6. In xy = k, k = ; when x = 2, y = .
Fill in each blank
Answer:
4.6 people take 22 days over a job. Working as fast, 11 people take days
Answer:
5.y is in inverse proportion to x: when x = 6, y = 8; when x = 8, y = ; when x = , y = 2.
Fill in each blank
Answer:
6.At 60 km/h the trip takes 2 hours. To cover the same distance in 6 hours, the speed must be km/h
Answer:
7.y is in inverse proportion to x: when x = 2, y = 24; when x = 12, y = ; when x = , y = 8.
Fill in each blank
Answer:
8.4 machines take 10 hours over a batch of work. After 5 hours, 1 more machines of the same kind join. How many more hours does the rest take?
Answer:

9.In which set of values is y in inverse proportion to x?
- A. (x, y) = (1, 31), (2, 16), (4, 8)
- B. (x, y) = (1, 36), (2, 22), (4, 15)
- C. (x, y) = (1, 7), (2, 14), (4, 28)
- D. (x, y) = (1, 28), (2, 14), (4, 7)
Choose the right answer
Answer:
10.y is in inverse proportion to x. When x = 5, y = 32, so when x = 20, y = 128.
True or false?
Answer:
11.y is in inverse proportion to x. If x goes up 60%, what happens to y?
- A. It goes up 60%
- B. It goes down 37.5%
- C. It goes down 60%
- D. It stays the same
Choose the right answer
Answer:
12.y is in inverse proportion to x. If x goes up 25%, what happens to y?
- A. It goes up 25%
- B. It goes down 25%
- C. It goes down 20%
- D. It stays the same
Choose the right answer
Answer:

13.2 identical pumps working together empty a pond in 12 hours. How many hours do 6 such pumps take?
- A. 36 hours
- B. 8 hours
- C. 12 hours
- D. 4 hours
Choose the right answer
Working:
Answer:
14.At 80 km/h it takes 6 hours to drive from P to Q. If the speed goes up 300%, how many hours does it take?
Working:
Answer:
15.9 people take 18 days over a job, all working as fast, so 27 people take 6 days.
True or false?
Working:
Answer:
16.A store of food feeds 50 people for 24 days. If 10 more people share it, how many days does it last?
Working:
Answer:
17.16 workers take 10 days over a project. It is person-days of work; to finish in 4 days needs workers.
Fill in each blank
Working:
Answer:
18.9 people take 20 days over a job. With only 2 people, how many more days does it take? Put the steps in order.
- A. 90 − 20 = 70
- B. 9 × 20 = 180
- C. 180 ÷ 2 = 90
Write the letters in the right order
Working:
Answer:

Show the answers and working

Inverse proportion worksheet: Answers and working

1. 6, 3
k = xy = 3 × 2 = 6; y = 6 ÷ 2 = 3.
2. 6
The whole job is 8 × 3 = 24 person-days, and 24 ÷ 4 = 6 days.
3. 18, 9
k = xy = 6 × 3 = 18; y = 18 ÷ 2 = 9.
4. 12
The whole job is 6 × 22 = 132 person-days, and 132 ÷ 11 = 12 days.
5. 6, 24
xy = 6 × 8 = 48: y = 48 ÷ 8 = 6, and x = 48 ÷ 2 = 24.
6. 20
Over the same distance, speed and time are inversely proportional: 60 × 2 = 120 km, and 120 ÷ 6 = 20 km/h.
7. 4, 6
xy = 2 × 24 = 48: y = 48 ÷ 12 = 4, and x = 48 ÷ 8 = 6.
8. 4 hours
The batch is 4 × 10 = 40 machine-hours; 4 × 5 are done, 20 are left, and 5 machines take 20 ÷ 5 = 4 hours.

9. D. (x, y) = (1, 28), (2, 14), (4, 7)
Inverse proportion needs the same x × y for every pair: 1 × 28 = 2 × 14 = 4 × 7 = 28.
10. False
x becomes 4 times as much, so y becomes 14 of it: 32 ÷ 4 = 8. Check: 5 × 32 = 20 × 8.
11. B. It goes down 37.5%
xy stays: x becomes 1 + 60% times as much, so y becomes 1 ÷ (1 + 60%) of it, down 60 ÷ (100 + 60) × 100% = 37.5%.
12. C. It goes down 20%
xy stays: x becomes 1 + 25% times as much, so y becomes 1 ÷ (1 + 25%) of it, down 25 ÷ (100 + 25) × 100% = 20%.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. D. 4 hours
The job is 2 × 12 = 24 pump-hours, and 24 ÷ 6 = 4 hours.
14. 1.5 hours
The new speed is 80 × (1 + 300%) = 320 km/h. The distance stays, so time is inversely proportional to speed: 80 × 6 ÷ 320 = 1.5 hours.
15. True
3 times the people take 13 of the time: 18 ÷ 3 = 6 days.
16. 20 days
The food is 50 × 24 = 1200 person-days; with 60 people, 1200 ÷ 60 = 20 days.
17. 160, 40
16 × 10 = 160 person-days, and 160 ÷ 4 = 40 workers.
18. B → C → A
The whole job first, then ÷ the new number of people, then compare with the old time.

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