CLASS 8 • MATHEMATICS • PRACTICE PAPER
Proportional Reasoning – Practice Paper
Direct Proportion • Inverse Proportion • Ratios • Applications
Class 8 Maths – Proportional Reasoning Practice
This Class 8 Mathematics practice paper gives students focused practice on direct proportion, inverse proportion, unitary reasoning, speed and time, work and workers, cost and quantity, map scales and other real-life applications of proportional relationships.
The paper moves from quick MCQs to short numericals, multi-step problems and case-based questions. Students should show their working clearly, identify the type of proportion involved and check whether the final answer is reasonable.
Key skills: Direct Proportion • Inverse Proportion • Constant Ratio • Constant Product • Unit Conversion • Speed • Work & Time • Scale • Logical Reasoning
Class 8 Mathematics
Practice Paper
Topic: Proportional Reasoning
Section A: Multiple Choice Questions 1 × 20 = 20 marks
Choose the correct option for each question.
1
If the cost of 8 kg of rice is ₹320, what is the cost of 5 kg of rice?
a) ₹180
b) ₹200
c) ₹220
d) ₹240
2
Which of the following represents an inverse proportion?
a) Cost and quantity
b) Speed and time for a fixed distance
c) Distance and time
d) Wages and days
3
If 12 workers take 10 days to complete a work, how many days will 6 workers take?
4
If x ∝ y, which of the following remains constant?
a) x + y
b) x − y
c) x ÷ y
d) x × y
5
A car travels 240 km using 16 litres of petrol. How far will it travel using 10 litres?
a) 120 km
b) 140 km
c) 150 km
d) 160 km
6
If 4 pipes fill a tank in 12 hours, how long will 8 pipes take?
a) 24 hours
b) 12 hours
c) 6 hours
d) 4 hours
7
If 15 notebooks cost ₹225, find the cost of 4 notebooks.
a) ₹50
b) ₹55
c) ₹60
d) ₹65
8
When the number of workers increases while the amount of work stays the same, the time required will:
a) Increase
b) Decrease
c) Remain the same
d) Become zero
9
If 6 kg of apples cost ₹360, what is the cost of 9 kg?
a) ₹480
b) ₹510
c) ₹540
d) ₹600
10
If x × y is constant, then x and y are in:
a) Direct proportion
b) Inverse proportion
c) No proportion
d) Equal proportion
11
A train covers 90 km in 2 hours. How much distance will it cover in 5 hours?
a) 180 km
b) 200 km
c) 225 km
d) 250 km
12
If 10 men can complete a job in 18 days, how many men are needed to finish it in 9 days?
13
If 7 books weigh 2.1 kg, what is the weight of 10 such books?
a) 2.5 kg
b) 3 kg
c) 3.2 kg
d) 3.5 kg
14
For a fixed distance, speed and time are related by:
a) Direct proportion
b) Inverse proportion
c) Constant ratio
d) No relation
15
A map has a scale of 1 : 50,000. What actual distance is represented by 4 cm?
a) 2 km
b) 4 km
c) 8 km
d) 10 km
16
A worker earns ₹750 in 15 days. How much will he earn in 20 days?
a) ₹900
b) ₹950
c) ₹1,000
d) ₹1,050
17
If 24 taps fill a tank in 5 hours, how many taps are required to fill it in 10 hours?
18
If the cost of 12 pens is ₹180, what is the cost of 20 pens?
a) ₹250
b) ₹270
c) ₹300
d) ₹320
19
Which quantity remains constant in inverse proportion?
a) Ratio
b) Difference
c) Sum
d) Product
20
A car travels 150 km in 3 hours. What is its speed?
a) 40 km/h
b) 45 km/h
c) 50 km/h
d) 60 km/h
Section B: Short Answer Numericals 2 × 10 = 20 marks
Solve each problem and show the important steps.
21
If 9 kg of wheat costs ₹270, find the cost of 14 kg.
22
A train covers 360 km in 6 hours. How long will it take to cover 540 km at the same speed?
23
If 15 workers complete a work in 16 days, how many days will 20 workers take?
24
The cost of 18 chairs is ₹7,200. Find the cost of 25 chairs.
25
8 pumps can empty a tank in 12 hours. How long will 6 pumps take?
26
If 5 litres of petrol allows a car to travel 80 km, how far will it travel using 9 litres?
27
The scale of a map is 1 : 20,000. Find the actual distance represented by 7 cm.
28
A worker is paid ₹960 for 12 days. How much will he earn for 20 days?
29
If 16 machines manufacture 4,800 bolts in a day, how many bolts will 10 machines manufacture?
30
If 30 students can finish food in 18 days, how long will the food last for 45 students?
Section C: Long Answer Numericals 4 × 5 = 20 marks
Show your complete working and state the proportion used.
31
A bus travels at a speed of 60 km/h and takes 7 hours to reach its destination.
(a) Find the distance covered.
(b) How long will it take to cover the same distance at 75 km/h?
32
24 workers can complete a work in 15 days.
(a) How many workers are needed to complete the work in 10 days?
(b) How many days will 30 workers take to complete the same work?
33
In a hostel, food is sufficient for 200 students for 25 days. After 5 days, 50 students leave the hostel. For how many more days will the remaining food last?
34
The extension of a spring varies directly with the load applied. If a load of 3 kg produces an extension of 5 cm, find:
(a) Extension produced by 7.5 kg.
(b) Load required to produce an extension of 12 cm.
Section D: Case-Based Questions 5 × 4 = 20 marks
35
A factory produces goods using machines.
| Machines |
8 |
12 |
20 |
| Days |
15 |
? |
6 |
Answer the following:
(a) Identify the type of proportion.
(b) Find the missing number of days.
(c) Write the formula used.
(d) What happens to the time if the number of machines increases further?
36
A car covers a fixed distance.
| Speed (km/h) |
50 |
75 |
? |
| Time (h) |
6 |
4 |
3 |
Use the table to reason about the relationship between speed and time for a fixed distance.
Practice • Solve • Improve
Try the complete paper yourself before checking your solutions. For more Class 8 Maths practice and explanations:
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