RATES AND VARIATIONS REVISION QUESTIONS

(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

16. If y varies directly as x, and y = 10 when x = 5, find y when x = 8.
17. If y ∝ 1/x and y = 6 when x = 2, find x when y = 3.
18. If y varies as the square of x and y = 18 when x = 3, find y when x = 5.
19. If y varies inversely as x and y = 12 when x = 4, find x when y = 6.
20. If y varies directly with x and y = 30 when x = 10, find x when y = 45.
21. If y ∝ x² and y = 16 when x = 2, what is x when y = 64?
22. If y = kx and y = 24 when x = 6, find k and y when x = 9.
23. If y ∝ √x and y = 10 when x = 25, find y when x = 100.
24. If y varies inversely with √x, and y = 4 when x = 9, find y when x = 36.
25. If A ∝ B and A = 7 when B = 2, find A when B = 10.
26. If T ∝ D² and T = 100 when D = 5, find T when D = 8.
27. If volume V ∝ cube of radius r, and V = 27 when r = 3, find V when r = 6.
28. If speed is inversely proportional to time, and speed = 60 km/h when time = 2 h, what is speed when time = 1.5 h?
29. If y = k/x and y = 5 when x = 4, what is y when x = 10?
30. If y ∝ x and x = 3 gives y = 12, what is y when x = 5?
31. 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.
32. 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.
33. If y ∝ x² and inversely as z, and y = 18 when x = 3 and z = 2, find y when x = 6 and z = 4.
34. If y ∝ √xz and y = 12 when x = 9 and z = 16, find y when x = 4 and z = 36.
35. 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.
36. If y ∝ x/z² and y = 4 when x = 8 and z = 2, find y when x = 18 and z = 3.
37. 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.
38. If y ∝ xz² and y = 100 when x = 5 and z = 2, find y when x = 4 and z = 3.
39. If y ∝ x³/z and y = 27 when x = 3 and z = 1, find y when x = 2 and z = 4.
40. 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