How many practice questions are available for Direct & Inverse Proportions?

SparkEd Math offers 60+ practice questions for Direct & Inverse Proportions across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Direct & Inverse Proportions content free on SparkEd Math?

Yes! All Direct & Inverse Proportions content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Direct & Inverse Proportions differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Direct & Inverse Proportions problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Direct & Inverse Proportions content aligned with the CBSE syllabus?

Yes, all Direct & Inverse Proportions questions and lessons on SparkEd Math are fully aligned with the Central Board of Secondary Education (CBSE) syllabus for Class 8. The content follows the official curriculum structure and exam pattern.

Direct & Inverse Proportions — Class 8 CBSE (2025-26)

About Direct & Inverse Proportions — Class 8 CBSE

Identify and solve problems involving direct and inverse proportion. This topic is part of the CBSE Class 8 mathematics syllabus (chapter: Chapter 7). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Direct & Inverse Proportions

Introduction to Proportions: Direct Relationships
Understanding Direct Proportion with Constant 'k'
Introduction to Inverse Proportions
Understanding Inverse Proportion with Constant 'k'
Comparing & Applying Direct and Inverse Proportions

Interactive lesson · about 15 minutes · checkpoint question after every unit

Direct & Inverse Proportions — solved examples for Class 8 CBSE

Example 1easy

Which of the following statements is TRUE regarding two quantities, x and y, that are directly proportional?

A)As x increases, y decreases.
B)The ratio x/y remains constant.
C)The product x × y remains constant.
D)Their sum x + y remains constant.

Step-by-step solution

Step 1: Understand direct proportion. Two quantities are directly proportional if an increase in one leads to a proportional increase in the other, and a decrease in one leads to a proportional decrease in the other.
Step 2: The defining characteristic of direct proportion is that their ratio (x/y) is always constant. This constant is called the constant of proportionality.
$x/y = k (where k is the constant of proportionality)$

Answer: The ratio x/y remains constant.

Example 2medium

If 5 kg of a special paint costs ₹1250, how much would 12 kg of the same paint cost?

A)₹2500
B)₹3000
C)₹3500
D)₹4000

Step-by-step solution

First, find the cost of 1 kg of paint. Since 5 kg costs ₹1250, 1 kg costs ₹1250 / 5.
Cost of 1 kg paint = ₹250.
Now, to find the cost of 12 kg of paint, multiply the cost of 1 kg by 12.
$Cost of 12 kg = 12 × ₹250$
Cost of 12 kg = ₹3000.

Answer: ₹3000

Example 3hard

If quantity P is directly proportional to the square of quantity Q, and Q is inversely proportional to R, which of the following statements is true?

A)P is directly proportional to R²
B)P is inversely proportional to R
C)P is directly proportional to R
D)P is inversely proportional to R²

Step-by-step solution

P is directly proportional to Q² means P = k₁Q² for some constant k₁.
Q is inversely proportional to R means Q = k₂/R for some constant k₂.
Substitute Q = k₂/R into the first equation: P = k₁(k₂/R)² = k₁(k₂²/R²) = (k₁k₂²)/R².
Since k₁k₂² is a constant, P = Constant/R², which means P is inversely proportional to R².

Answer: P is inversely proportional to R²

Practice questions on Direct & Inverse Proportions

Q1.easy
Which of the following scenarios represents a direct proportion?
1. A)The speed of a car and the time it takes to cover a fixed distance.
2. B)The number of workers and the time taken to complete a fixed amount of work.
3. C)The amount of petrol filled in a car and the distance covered by the car.
4. D)The number of articles purchased and the discount received per article.
Show answer
Answer: The amount of petrol filled in a car and the distance covered by the car.
Hint: For direct proportion, as one quantity increases, the other should also increase proportionally.
Q2.easy
If the cost of 5 notebooks is ₹125, what will be the cost of 8 such notebooks?
1. A)₹150
2. B)₹175
3. C)₹200
4. D)₹225
Show answer
Answer: ₹200
Hint: The number of notebooks and their cost are directly proportional. Set up a ratio to solve.
Q3.easy
Rohan wanted to find the value of y when x=12, given that x and y are directly proportional. He knew that when x=4, y=10. His working was: (4 × 10) = (12 × y) => 40 = 12y => y = 40/12 = 10/3. What mistake did Rohan make?
1. A)He should have used (x + y) = constant.
2. B)He incorrectly assumed x and y are inversely proportional.
3. C)He made a calculation error in the final step.
4. D)He should have set up the equation as (4/10) = (12/y).
Show answer
Answer: He incorrectly assumed x and y are inversely proportional.
Hint: Recall the formula used for direct proportion versus inverse proportion. Rohan used the formula for inverse proportion.
Q4.medium
15 workers can complete a construction project in 40 days. If 5 more workers are hired, how many days will it take to complete the same project?
1. A)25 days
2. B)30 days
3. C)35 days
4. D)40 days
Show answer
Answer: 30 days
Hint: The number of workers and the time taken to complete a fixed task are in inverse proportion.
Q5.medium
Which of the following scenarios represents a direct proportion?
1. A)The number of workers and the time taken to complete a fixed task.
2. B)The speed of a car and the time taken to cover a fixed distance.
3. C)The amount of petrol filled in a car and the distance it can travel.
4. D)The number of identical books and the weight of each book.
Show answer
Answer: The amount of petrol filled in a car and the distance it can travel.
Hint: In direct proportion, as one quantity increases, the other quantity increases proportionally.
Q6.medium
Which of the following quantities are in inverse proportion?
1. A)Area of a square and its side length.
2. B)The number of hours a pump works and the amount of water it pumps.
3. C)The number of days required to build a wall and the number of masons working on it.
4. D)The cost of a commodity and the number of units purchased (at a fixed price per unit).
Show answer
Answer: The number of days required to build a wall and the number of masons working on it.
Hint: In inverse proportion, as one quantity increases, the other quantity decreases proportionally.
Q7.hard
Two quantities, A and B, are inversely proportional. If A increases by 20%, what is the percentage decrease in B?
1. A)16.67%
2. B)20%
3. C)25%
4. D)33.33%
Show answer
Answer: 16.67%
Hint: Remember that for inverse proportion, the product of the two quantities remains constant. Express the new value of A in terms of the original A.
Q8.hard
A construction team of 15 workers can build a wall 120 meters long in 8 days, working 6 hours a day. How many additional workers are needed to build a wall 160 meters long in 10 days, working 4 hours a day?
1. A)6
2. B)8
3. C)9
4. D)12
Show answer
Answer: 9
Hint: Use the compound proportion formula M₁D₁H₁/W₁ = M₂D₂H₂/W₂ where M is men, D is days, H is hours, and W is work.
Q9.hard
12 pipes can fill a tank in 10 hours. If 4 of these pipes are blocked, and the remaining pipes are now 20% less efficient due to scaling, how long will it take to fill the same tank?
1. A)12.5 hours
2. B)15 hours
3. C)18 hours
4. D)20 hours
Show answer
Answer: 18 hours
Hint: First, calculate the time it would take for the remaining pipes if they were 100% efficient. Then, consider how reduced efficiency affects the time taken.

These are 9 of the 60 questions available for Direct & Inverse Proportions. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.