DIRECT AND INVERSE VARIATION

 

Class 8 CBSE Mathematics Question Paper 1

Chapter: Direct and Inverse Variation

Maximum Marks: 40 | Time: 1.5 Hours

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Section A: Multiple Choice Questions (1 mark each)

1. If $x$ varies directly as $y$and $x = 8$ when $y = 4$, then what is the value of $\mathrm{xwhen }$$y = 10$?
   a) 16
   b) 20
   c) 10
   d) 12

2. If $x$ and $y$ are in inverse proportion and $x = 5$, $y = 10$, then when $x = 10$, $y$ will be:
   a) 20
   b) 5
   c) 15
   d) 25

3. If 6 workers take 8 days to complete a task, how many days will 4 workers take to complete the same task?
   a) 10
   b) 12
   c) 9
   d) 8

4. The number of men working on a project and the number of days required to complete it are in:
   a) Direct variation
   b) Inverse variation
   c) No variation
   d) None of these

5. If the speed of a vehicle increases, the time taken to cover the same distance:
   a) Increases
   b) Decreases
   c) Remains the same
   d) None of these

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Section B: Fill in the Blanks (1 mark each)

6. If $x$ and $y$ are in direct variation, then the ratio $\frac{x}{y}$ is ________.
7. If $x$ and $y$are in inverse variation, then the product $x\times \mathrm{y\; is\; \_\_\_\_\_\_\_\_.}$
8. The speed of a car and the time taken to cover a fixed distance are in ________ proportion.
9. If the cost of 5 kg of sugar is ₹200, then the cost of 8 kg of sugar is ________.
10. If the time taken to complete a task is inversely proportional to the number of workers, then more workers will take ________ time to complete the task.

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Section C: Short Answer Questions (2 marks each)

11. If 8 books cost ₹640, find the cost of 15 books assuming direct proportion.
12. A car travels 150 km in 3 hours. How much time will it take to travel 250 km at the same speed?
13. If $x$and $y$ vary inversely and $x = 6$ when $y = 12$, find $y$ when $x = 8$.
14. 12 men can complete a work in 20 days. How many days will 8 men take to complete the same work?
15. If a train moving at 60 km/h takes 5 hours to reach a destination, how long will it take if the speed is increased to 75 km/h?

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Section D: Long Answer Questions (4 marks each)

16. The cost of 5 meters of cloth is ₹450. Find the cost of 12 meters of cloth using direct proportion.
17. 6 pumps working together can empty a water tank in 12 hours. How long will 8 pumps take to empty the same tank?
18. If 3 workers can complete a task in 18 days, how many days will 9 workers take to complete the same task?
19. A cyclist travels 15 km in 30 minutes. How much distance will he travel in 2 hours at the same speed?
20. If 10 machines produce 500 units in 5 hours, how many units will 15 machines produce in 8 hours?

 

Question Paper 2

Section A: Multiple Choice Questions (1 mark each)

1. If $x$ and $y$ vary directly, and $x = 6$ when $y = 12$, what is $y$ when $x = 10$?
   a) 15
   b) 20
   c) 18
   d) 25

2. If 10 men take 15 days to complete a task, then 5 men will take:
   a) 30 days
   b) 20 days
   c) 10 days
   d) 25 days

3. The speed of a train and the time taken to cover a fixed distance are in:
   a) Direct proportion
   b) Inverse proportion
   c) No proportion
   d) Equal proportion

4. If 3 pens cost ₹60, then the cost of 7 pens is:
   a) ₹120
   b) ₹140
   c) ₹100
   d) ₹180

5. If $x$ and $y$ are in inverse proportion, then:
   a) $x \times y$= constant
   b) $\frac{x}{y}$ = constant
   c) $x + y$= constant
   d) None of these

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Section B: Fill in the Blanks (1 mark each)

6. If $x$ varies directly as $y$, then the equation is written as ________.
7. If 6 workers complete a work in 8 days, then 12 workers will complete it in ________ days.
8. If the number of workers increases, the time taken to complete the work ________.
9. If 4 kg of apples cost ₹200, then the cost of 10 kg of apples is ________.
10. If $x$ and $y$ are inversely proportional, and $x = 5$, $y = 20$, then when $x = 10$, $y$ will be ________.

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Section C: Short Answer Questions (2 marks each)

11. If 12 pens cost ₹180, find the cost of 5 pens assuming direct variation.
12. A car covers 240 km in 4 hours. How much time will it take to cover 360 km at the same speed?
13. If $x$ and $y$ vary inversely and $x = 8$ when $y = 16$, find $y$ when $x = 4$.
14. 15 men can construct a wall in 10 days. How long will it take for 25 men to do the same work?
15. A bus traveling at 50 km/h takes 6 hours to reach its destination. How much time will it take if the speed is increased to 75 km/h?

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Section D: Long Answer Questions (4 marks each)

16. The cost of 9 meters of cloth is ₹810. Find the cost of 15 meters of cloth using direct proportion.
17. If 5 machines produce 600 units in 8 hours, how many units will 7 machines produce in 10 hours?
18. A train covers 300 km in 5 hours. Find the time taken to cover 450 km at the same speed.
19. If 6 pipes fill a tank in 12 hours, how much time will 8 pipes take to fill the same tank?
20. A group of 20 workers can complete a task in 30 days. If 5 more workers join the group, how many days will they take to complete the task?