Class 8

chapter-11

Direct and Inverse Proportion

20 Multiple Choice Questions (MCQs)
1. If 5 pens cost ₹25, how much will 8 pens cost at the same rate?
(a) ₹35
(b) ₹40
(c) ₹45
(d) ₹50
2. Which of the following pairs are in direct proportion?
(a) Speed and time
(b) Number of workers and time
(c) Cost and quantity
(d) Distance and speed
3. If x increases and y increases as well, the relationship is called:
(a) Direct proportion
(b) Inverse proportion
(c) No proportion
(d) None
4. Two quantities x and y are in inverse proportion if:
(a) x × y = constant
(b) x/y = constant
(c) x + y = constant
(d) x - y = constant
5. If 3 workers can complete a job in 6 days, how many workers
are needed to complete it in 2 days?
 (a) 6
(b) 9
(c) 12
(d) 3
6. If 4 metres of cloth costs ₹200, what will 10 metres cost?
(a) ₹400
(b) ₹450
(c) ₹500
(d) ₹600
7. The number of workers and the time taken to complete a job are
in:
(a) Direct proportion
(b) Inverse proportion
(c) No relation
(d) Equal proportion
8. If speed increases, time taken for fixed distance:
(a) Increases
(b) Decreases
(c) Remains same
(d) Doubles
9. When quantity A increases, quantity B decreases. It is:
(a) Direct proportion
(b) Inverse proportion
(c) No proportion
(d) Equal proportion
10. If a car travels 60 km in 1 hour, how long will it take to travel
180 km?
(a) 1 hour
(b) 2 hours
 (c) 3 hours
(d) 4 hours
11. Which is a feature of inverse proportion?
(a) Sum is constant
(b) Product is constant
(c) Difference is constant
(d) Ratio is constant
12. In direct proportion, the ratio x/y is:
(a) Constant
(b) Increases
(c) Decreases
(d) Variable
13. If 7 notebooks cost ₹210, the cost of 1 notebook is:
(a) ₹20
(b) ₹25
(c) ₹30
(d) ₹35
14. If 6 litres of oil costs ₹420, the cost of 9 litres is:
(a) ₹560
(b) ₹630
(c) ₹720
(d) ₹840
15. If time increases, speed must ______ to cover a fixed
distance.
(a) Increase
(b) Decrease
(c) Remain same
(d) Stop
16. Which example shows direct proportion?
(a) Speed and time
 (b) Cost and quantity
(c) Distance and time
(d) Area and perimeter
17. If x × y = constant, then x and y are in:
(a) Direct proportion
(b) Inverse proportion
(c) Equal proportion
(d) None
18. Which equation represents inverse proportion?
(a) x/y = k
(b) x × y = k
(c) x + y = k
(d) x = y
19. If a machine makes 10 items in 2 hours, how many in 6
hours?
(a) 20
(b) 25
(c) 30
(d) 35
20. Which of the following does not show direct proportion?
(a) Distance and time
(b) Cost and quantity
(c) Speed and time
(d) Salary and hours worked

Fill in the Blanks

1. Two quantities are said to be in direct proportion if their
______ is constant.
2. Two quantities are in inverse proportion if their ______ is
constant.
3. If x and y are in direct proportion, then (x1/x2) = (y1/y2).
4. If x and y are in inverse proportion, then x1 × y1 = x2 × y2.
5. When speed increases, time taken to cover the same distance
______.
6. If 5 workers complete a job in 6 days, then 10 workers will
complete it in ______ days.
7. The cost of 3 pens is ₹60. The cost of 5 pens is ₹______.
8. If 4 machines can produce 100 units in 5 days, then 8
machines will produce ______ units in 5 days.
9. If 6 men complete a work in 12 days, then 3 men will
complete the same work in ______ days.
10. In direct proportion, when one quantity increases, the other
quantity also ______.
11. The number of taps and the time taken to fill a tank are in
______ proportion.
12. Speed and time taken to cover a fixed distance are in ______
proportion.
13. Number of hours worked and total wages earned are in
______ proportion.
14. Number of workers and time taken to complete a job are in
______ proportion.
15. The area of land ploughed and number of hours worked are
in ______ proportion.
16. If a car covers 240 km in 4 hours, then it covers ______ km
in 6 hours.
17. If 12 men can build a wall in 10 days, then 6 men can build
it in ______ days.
18. Time taken to travel a fixed distance is ______ proportional
to the speed.
19. If cost of 5 kg sugar is ₹200, then cost of 8 kg is ₹______.
 20. The number of books and their total cost are in ______
proportion.

Very Short Answer Type Questions

1. Define direct proportion.
2. Define inverse proportion.
3. Write the condition for two quantities to be in direct
proportion.
4. Write the condition for inverse proportion.
5. What is the value of x if x : 12 = 3 : 4?
6. If 6 notebooks cost ₹90, what is the cost of 1 notebook?
7. If 5 litres of petrol cost ₹525, what is the cost of 1 litre?
8. Write the formula for direct proportion.
9. Write the formula for inverse proportion.
10. If 3 workers finish a task in 12 days, how many days will 6
workers take?
11. If 15 men can do a work in 8 days, how many days will 10
men take?
12. If 10 oranges cost ₹60, what is the cost of 25 oranges?
13. A train travels 180 km in 3 hours. What is the speed?
14. If 8 men build a wall in 24 days, how many days will 4 men
take?
15. If 5 pens cost ₹75, what is the cost of 1 pen?
16. If 2 machines produce 120 items in 4 days, how many items
will 4 machines produce in same time?
17. Write one real-life example of direct proportion.
18. Write one real-life example of inverse proportion.
19. A bus takes 5 hours to cover a distance at a speed of 40
km/h. How much distance will it cover?
 20. If 6 workers take 20 days to complete a task, how many
days will 12 workers take?

Short Answer Type Questions

1. Check whether the following pairs of quantities are in direct
or inverse proportion: speed and time.
2. A car travels 60 km in 1.5 hours. How long will it take to
travel 180 km at the same speed?
3. If 8 men complete a work in 15 days, how many men are
required to complete the same work in 10 days?
4. A printing press prints 6000 pages in 8 hours. How many
pages can it print in 12 hours?
5. If 20 workers can dig a trench in 6 days, how many days will
15 workers take?
6. If 9 bags of rice cost ₹1350, what will 6 bags cost?
7. If the cost of 7 metres of cloth is ₹630, find the cost of 5
metres of the same cloth.
8. If 5 men or 7 women can complete a work in 12 days, how
many days will 10 men take?
9. A car travels 120 km in 2.5 hours. Find its speed.
10. If 15 men can build a wall in 30 days, how many men are
required to build it in 10 days?
11. If 3 pipes can fill a tank in 6 hours, how long will 6 pipes
take?
12. If a train travels 540 km in 9 hours, find the time to travel
300 km.
13. A car covers a distance in 5 hours at 60 km/h. What time
will it take at 75 km/h?
14. 4 pumps can empty a tank in 8 hours. How many hours will
2 pumps take?
 15. A worker earns ₹400 in 8 hours. How much will he earn in
12 hours?
16. If 6 boys can complete a task in 9 days, in how many days
will 3 boys complete the task?
17. If 10 labourers can do a job in 12 days, how long will 15
labourers take?
18. A scooter runs 45 km in 1.5 hours. How long will it take to
run 90 km?
19. If 7 cows eat a certain amount of fodder in 4 days, how long
will 14 cows take to eat the same amount?
20. If 5 litres of milk cost ₹250, what is the cost of 12 litres?

Long Answer Type Questions

1. A car covers a distance of 540 km in 6 hours. How much time
will it take to cover 810 km at the same speed?
2. 8 men can build a wall in 15 days. How many men are
required to build the same wall in 10 days?
3. A train travels 180 km in 3 hours. At the same speed, how
long will it take to cover 450 km?
4. A worker earns ₹600 for 8 hours of work. How much will he
earn for 15 hours?
5. If 4 students can prepare 200 charts in 5 days, how many
charts can 8 students prepare in the same time?
6. 12 pipes can fill a tank in 6 hours. How many hours will 8
pipes take to fill the same tank?
7. A machine fills 120 bottles in 6 hours. How many bottles will
it fill in 15 hours?
8. If the cost of 9 kg of rice is ₹270, find the cost of 15 kg.
9. A car takes 3 hours to cover a distance at 60 km/h. How
much time will it take at 80 km/h?
 10. 5 men complete a task in 12 days. How long will 15 men
take to do the same task?
11. 7 boys can dig a pit in 21 days. In how many days will 3
boys dig it?
12. A cyclist travels 36 km in 3 hours. At the same speed, how
far will he travel in 5 hours?
13. If the cost of 7 metres of cloth is ₹875, what is the cost of
12 metres?
14. A farmer has enough food for 30 cows for 20 days. How
many days will the same food last for 50 cows?
15. If 6 men can build a wall in 20 days, how many men are
required to build the same wall in 15 days?
16. A train moves at a speed of 60 km/h. How much distance
will it cover in 4.5 hours?
17. A car covers 225 km in 3 hours. Find the time required to
cover 375 km at the same speed.
18. If 15 men can finish a work in 24 days, in how many days
will 20 men finish the same work?
19. 10 workers take 16 days to finish a job. How many days will
8 workers take?
20. If 9 notebooks cost ₹270, what is the cost of 12 notebooks?
10 Case-Based Studies
Case Study 1: A car travels 60 km in 1 hour. At the same speed,
how far will it travel in 4 hours?
 What type of proportion is involved here?
 Calculate the distance travelled.
Case Study 2: A shopkeeper sells 2 kg of rice for ₹100. How much
will he charge for 7 kg?
 Which proportion is used here?
 Find the total cost.
Case Study 3: 5 workers can build a wall in 10 days. If 10 workers
are employed, how many days will it take?
 Identify the proportion.
 Find the number of days.
Case Study 4: A bike covers 120 km in 3 hours. How long will it
take to cover 240 km at the same speed?
 State the proportion type.
 Find the required time.
Case Study 5: A factory produces 1000 units in 5 days using 4
machines. How many machines are required to produce 2000 units
in 5 days?
 Which proportion applies?
 Calculate the number of machines.
Case Study 6: A child drinks 2 litres of milk every 5 days. How
much milk will he drink in 20 days?
 What kind of proportion is involved?
 Find the total milk consumed.
Case Study 7: If 8 students can clean a hall in 6 hours, how long
will 12 students take?
 Determine the type of proportion.
 Calculate the required time.
Case Study 8: A train travels at 80 km/h. How much time will it
take to cover 640 km?
 What type of proportion is shown?
 Find the time taken.
Case Study 9: The cost of 4 pens is ₹80. What will be the cost of
10 pens?
 Is this direct or inverse proportion?
 Find the cost.
Case Study 10: If 3 pumps can fill a tank in 12 hours, how many
pumps are needed to fill the tank in 4 hours?
 Identify the proportion.
 Calculate the number of pumps.
10 OTS (Higher Order Thinking Skills)
1. Explain how time and speed are related using inverse
proportion in daily travel.
2. Why does doubling the number of workers halve the work
time in inverse proportion?
3. Is it possible for two variables to be neither directly nor
inversely proportional? Justify.
4. If cost per kg increases, what happens to the total cost for
fixed weight? Explain with example.
5. A car travels half the distance in twice the time. Is this direct
or inverse proportion? Explain.
6. Why is the relationship between number of taps and time to
fill a tank inverse proportion?
7. When more people work on a task, how is less time justified
mathematically?
8. Explain why cost and quantity purchased are directly
proportional with a graph sketch.
9. Give a real-life situation where inverse proportion does not
hold even when it seems so.
10. Is the relationship between number of children and
sweets shared direct or inverse? Explain.
10 MOTS (Middle Order Thinking Skills)
1. What is meant by direct proportion? Give one example.
2. Define inverse proportion with a suitable example.
3. If 3 pens cost ₹60, what is the cost of 5 pens?
4. If 4 students can do a task in 12 days, how long will 6
students take?
5. If speed = 60 km/h and time = 2 hours, find the distance.
6. If 8 metres of cloth costs ₹560, what is the cost of 5 metres?
7. Two variables have constant ratio. What kind of proportion is
this?
8. If a × b = constant, then a and b are in ______ proportion.
9. If 5 machines complete a job in 4 hours, how long will 10
machines take?
10. Write two differences between direct and inverse
proportion.

Flow diagram
match the following