Direct and Inverse variations

Class 8


TEST - 1

Instructions:

  • Each correct answer carries the specified marks.
  • No negative marking.
  • Show all workings clearly.


Total Marks: 40                                                                                           Max. Time: 2 hours    


Section A: Multiple Choice Questions (10 marks)


1. If y varies directly with x and y = 15 when x = 5, what is the value of y when x = 8?

   - A) 24

   - B) 30

   - C) 18

   - D) 12


2. If y varies inversely with x and y = 10 when x = 4, what is the value of y when x = 6?

   - A) 6

   - B) 15

   - C) 20

   - D) 8


3. If y varies directly with x and y = 24 when x = 6, what is the value of y when x = 12?

   - A) 48

   - B) 36

   - C) 72

   - D) 18


4. If y varies inversely with x and y = 8 when x = 4, what is the value of y when x = 10?

   - A) 3.2

   - B) 2.5

   - C) 1.6

   - D) 4


5. If y varies directly with x and y = 9 when x = 3, what is the value of y when x = 10?

   - A) 3

   - B) 30

   - C) 90

   - D) 27


6. If y varies inversely with x and y = 12 when x = 3, what is the value of y when x = 5?

   - A) 6

   - B) 4

   - C) 10

   - D) 3


7. If y varies directly with x and y = 40 when x = 10, what is the value of y when x = 20?

   - A) 80

   - B) 20

   - C) 160

   - D) 400


8. If y varies inversely with x and y = 15 when x = 3, what is the value of y when x = 6?

   - A) 7.5

   - B) 10

   - C) 5

   - D) 20


9. If y varies directly with x and y = 18 when x = 9, what is the value of y when x = 24?

   - A) 48

   - B) 36

   - C) 16

   - D) 72


10. If y varies inversely with x and y = 9 when x = 6, what is the value of y when x = 12?

    - A) 4.5

    - B) 18

    - C) 3

    - D) 2.25


Section B: Short Answer Questions (10 marks)


1. If y varies directly with x and y = 25 when x = 5, find y when x = 10.


2. If y varies inversely with x and y = 12 when x = 4, find y when x = 8.


3. If y varies directly with x and y = 36 when x = 9, find y when x = 12.


4. If y varies inversely with x and y = 16 when x = 2, find y when x = 8.


5. If y varies directly with x and y = 20 when x = 5, find y when x = 8.


Section C: Word Problems (20 marks)


1. If x varies inversely with y and x = 6 when y = 3, find x when y = 4.


2. If x varies directly with y and x = 18 when y = 3, find x when y = 6.


3. The time taken to complete a journey varies inversely with the speed of the vehicle. If a journey takes 6 hours at a speed of 40 km/h, how long will it take at a speed of 60 km/h?


4. The number of workers required to complete a job varies inversely with the time taken. If 8 workers can complete a job in 12 days, how many days will 12 workers take to complete the same job?





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