RATES AND VARIATIONS REVISION QUESTIONS

Rates and Variations Practice

(A) Rates – Questions 1 to 15

  1. A car travels 240 km in 3 hours. What is its speed in m/s?
  2. If a pipe fills a tank in 6 hours, how long will 3 such pipes take to fill it?
  3. A worker earns TZS 480 for 8 hours. What is the rate per minute?
  4. 5 liters of paint cover 20 m². How much paint is needed to cover 100 m²?
  5. A man runs 12 km in 1 hour 36 minutes. What is his average speed in km/h?
  6. A 2 kg packet of sugar costs TZS 4. What’s the cost per gram?
  7. Three people can complete a task in 4 days. How many days will 6 people take?
  8. A train travels 180 km in 2.5 hours. What’s its speed in m/s?
  9. It takes 6 taps 2 hours to fill a tank. How long would 4 taps take?
  10. A factory produces 1,200 units in 6 hours. What’s the rate per minute?
  11. John earns TZS 50 per hour. If he works 7.5 hours, how much does he earn?
  12. A 100 ml bottle of oil costs TZS 3. What is the price per liter?
  13. A school bus covers 75 km in 1 hour 40 minutes. Find the average speed in km/h.
  14. It takes 9 workers 10 days to complete a building. How long will 6 workers take?
  15. A cyclist travels 45 km in 1.5 hours. What is the speed in m/s?

(B) Variations – Questions 16 to 40

  1. If y varies directly as x, and y = 10 when x = 5, find y when x = 8.
  2. If y ∝ 1/x and y = 6 when x = 2, find x when y = 3.
  3. If y varies as the square of x and y = 18 when x = 3, find y when x = 5.
  4. If y varies inversely as x and y = 12 when x = 4, find x when y = 6.
  5. If y varies directly with x and y = 30 when x = 10, find x when y = 45.
  6. If y ∝ x² and y = 16 when x = 2, what is x when y = 64?
  7. If y = kx and y = 24 when x = 6, find k and y when x = 9.
  8. If y ∝ √x and y = 10 when x = 25, find y when x = 100.
  9. If y varies inversely with √x, and y = 4 when x = 9, find y when x = 36.
  10. If A ∝ B and A = 7 when B = 2, find A when B = 10.
  11. If T ∝ D² and T = 100 when D = 5, find T when D = 8.
  12. If volume V ∝ cube of radius r, and V = 27 when r = 3, find V when r = 6.
  13. If speed is inversely proportional to time, and speed = 60 km/h when time = 2 h, what is speed when time = 1.5 h?
  14. If y = k/x and y = 5 when x = 4, what is y when x = 10?
  15. If y ∝ x and x = 3 gives y = 12, what is y when x = 5?
  16. If y varies directly as x and inversely as z, and y = 6 when x = 3 and z = 2, find y when x = 4 and z = 1.
  17. If y varies jointly as x and z, and y = 24 when x = 2 and z = 6, find y when x = 3 and z = 8.
  18. If y ∝ x² and inversely as z, and y = 18 when x = 3 and z = 2, find y when x = 6 and z = 4.
  19. If y ∝ √xz and y = 12 when x = 9 and z = 16, find y when x = 4 and z = 36.
  20. If y varies directly as the product of x and z, and y = 15 when x = 3 and z = 5, find y when x = 6 and z = 2.
  21. If y ∝ x/z² and y = 4 when x = 8 and z = 2, find y when x = 18 and z = 3.
  22. If y varies jointly as x² and z, and y = 72 when x = 3 and z = 4, find y when x = 6 and z = 2.
  23. If y ∝ xz² and y = 100 when x = 5 and z = 2, find y when x = 4 and z = 3.
  24. If y ∝ x³/z and y = 27 when x = 3 and z = 1, find y when x = 2 and z = 4.
  25. If y is inversely proportional to the product of x and z, and y = 5 when x = 2 and z = 3, find y when x = 5 and z = 1.

📝 Answers

  1. 22.22 m/s
  2. 2 hours
  3. TZS 1 per minute
  4. 25 liters
  5. 7.5 km/h
  6. TZS 0.002 per gram
  7. 2 days
  8. 20 m/s
  9. 3 hours
  10. 3.33 units/min
  11. TZS 375
  12. TZS 30
  13. 45 km/h
  14. 15 days
  15. 8.33 m/s
  16. 16
  17. 4
  18. 50
  19. 8
  20. 15
  21. k = 4, y = 36
  22. 20
  23. 2
  24. 35
  25. 256
  26. 216
  27. 80 km/h
  28. 2
  29. 20
  30. 20
  31. 12
  32. 36
  33. 81
  34. 12
  35. 18
  36. 8
  37. 288
  38. 144
  39. 2
  40. 0.6

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