Direct and Inverse Proportions quiz

If x and y are in direct proportion, then:

Which pair of quantities is in inverse proportion?

If 4 pens cost Rs 60, the cost of 7 such pens is:

If 8 workers can finish a job in 12 days, then 6 workers will finish it in:

If y = 5x, then y is:

On a map, 1 cm represents 5 km. A distance of 6 cm on the map represents:

If x and y are in inverse proportion and x is doubled, then y is:

x and y are in inverse proportion. When x = 4, y = 6. When x = 8, y is:

The graph of two quantities in direct proportion is:

A train at 75 km/h covers a distance in 4 hours. At 100 km/h it will cover the same distance in:

Explain inverse proportion using the example of speed and time taken for a fixed journey. (2 marks)

If 12 kg of rice costs Rs 600, find the cost of 20 kg of rice. (2 marks)

Check whether x and y are in direct proportion for the pairs (1, 4), (2, 8), (3, 12) and (4, 16). If so, find the constant of proportionality. (2 marks)

Ten taps fill a tank in 9 hours. How long will 6 such taps take to fill it? (2 marks)

A hostel has a fixed amount of food. Is the number of students in the hostel inversely proportional to the number of days the food lasts? Explain. (2 marks)

A machine fills 840 bottles in 6 hours. How many bottles will it fill in 5 hours? (2 marks)

x and y are in inverse proportion with x = 9 when y = 16. Find the constant of proportionality and the value of y when x = 12. (2 marks)

Rohan types 540 words in 15 minutes. How many words will he type in 1 hour at the same speed? (2 marks)

A photograph of a bacterium enlarged 50,000 times shows a length of 5 cm. What is the actual length of the bacterium? (2 marks)

Give two examples of pairs of quantities that change together but are neither in direct nor in inverse proportion. (2 marks)

A train is moving at a uniform speed of 75 km/h. (i) How far will it travel in 20 minutes? (ii) Find the time required to cover a distance of 250 km. (3 marks)

A contractor estimates that 3 persons could rewire a house in 4 days. If he uses 4 persons instead, how long should they take to complete the job? (3 marks)

A batch of bottles was packed in 12 boxes with 25 bottles in each box. If the same batch is packed using 20 bottles in each box, how many boxes would be filled? (3 marks)

In a model of a ship, the mast is 9 cm high, while the mast of the actual ship is 12 m high. If the length of the ship is 28 m, how long is the model ship? (3 marks)

A farmer has enough food to feed 20 animals in his cattle shed for 6 days. How long would the food last if there were 10 more animals in the shed? (3 marks)

Read the passage and answer the questions. Mr Sharma's car uses 25 litres of petrol to travel 500 km on the highway at a steady speed. (i) How much petrol will it need to travel 300 km? (ii) How far can it travel with 40 litres of petrol? (iii) What type of proportion is this? Find the constant of proportionality and state what it represents. (5 marks)

Read the passage and answer the questions. A school bus travelling at an average speed of 40 km/h takes 3 hours to reach a picnic spot. On the return journey the road is clear and the bus travels at 60 km/h. (i) Find the distance of the picnic spot from the school. (ii) How long does the return journey take? (iii) Name the type of proportion between speed and time here and state the constant. (5 marks)

Read the passage and answer the questions. A hostel has 100 students and enough provisions for 20 days. (i) If 25 more students join, how long will the provisions last? (ii) If instead 20 students leave, how long will the provisions last? (iii) Name the type of proportion involved and explain why. (5 marks)

Read the passage and answer the questions. A recipe for vegetable pulao for 4 people uses 300 g of rice and 2 tomatoes. Priya wants to cook it for a party. (i) How much rice and how many tomatoes are needed for 10 people? (ii) If she has 1.2 kg of rice, for how many people can she cook? (iii) Which type of proportion did you use? Give a reason. (5 marks)

Read the passage and answer the questions. A company employs 12 workers to lay a village road, and they can finish it in 15 days. (i) How many days would 20 workers take? (ii) How many workers are needed to finish the road in 10 days? (iii) What quantity stays constant in this situation? (5 marks)

Sugar costs Rs 45 per kg. Write the cost of 1, 2, 3, 4 and 5 kg of sugar and draw a graph of weight against cost. From the graph, find (i) the cost of 2.5 kg of sugar (ii) the weight of sugar that can be bought for Rs 180. Explain why the graph is a straight line through the origin. (6 marks)

A distance of 120 km is to be covered. Find the time taken at speeds of 20, 30, 40 and 60 km/h, and draw a graph of speed against time. Show that the product of speed and time is constant, and find the time taken at 48 km/h. (6 marks)

Explain the difference between direct and inverse proportion with two examples of each. Solve: (i) if 35 m of cloth costs Rs 2,100, find the cost of 52 m (ii) if 15 men can dig a canal in 40 days, how long will 25 men take? (6 marks)

A map has the scale 1 cm represents 2.5 km. (i) Two villages are 6.4 cm apart on the map; find the actual distance. (ii) A road of 40 km is to be shown on the map; find its length on the map. Draw a line segment 7 cm long showing the scale divisions and write the actual distance it represents. (6 marks)

A camp of 60 students has food for 24 days. After 4 days, 20 students leave the camp. For how many more days will the remaining food last? Draw a time line showing the days used and the days left, and explain each step of your solution. (6 marks)