Chapter 7 (Balbharati) · Class 8 Maharashtra SSC · MCQ Test

Variation (चलन) MCQ Test — Class 8 Maharashtra SSC

Practice 10 multiple-choice questions with instant answer reveal and explanations.

Variation (चलन) — MCQ Questions

1Which 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.
Show Answer+

Answer: The ratio x/y remains constant.

Hint: Recall the definition of direct proportionality and how the relationship between the quantities' values behaves.

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)

2Which of the following scenarios represents a direct proportion?

A.The speed of a car and the time it takes to cover a fixed distance.
B.The number of workers and the time taken to complete a fixed amount of work.
C.The amount of petrol filled in a car and the distance covered by the car.
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.

Solution:

Step 1: Analyze each option. A) As speed increases, time decreases (Inverse). B) As workers increase, time decreases (Inverse). C) As the amount of petrol increases, the distance covered increases proportionally (Direct). D) This relationship is not necessarily proportional in a simple direct or inverse way; discount per article might stay constant or change in a complex way.

Step 2: Identify the scenario where an increase in one quantity leads to a proportional increase in the other.

3If the cost of 5 notebooks is ₹125, what will be the cost of 8 such notebooks?

A.₹150
B.₹175
C.₹200
D.₹225
Show Answer+

Answer: ₹200

Hint: The number of notebooks and their cost are directly proportional. Set up a ratio to solve.

Solution:

Step 1: Let the number of notebooks be N and the cost be C. Since they are directly proportional, the ratio N/C remains constant. — N1/C1 = N2/C2

Step 2: Given N1 = 5, C1 = ₹125, N2 = 8. We need to find C2.

Step 3: Substitute the values: 5/125 = 8/C2.

Step 4: Solve for C2: 5 × C2 = 8 × 125 => C2 = (8 × 125) / 5 = 8 × 25 = ₹200.

4Rohan 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?

A.He should have used (x + y) = constant.
B.He incorrectly assumed x and y are inversely proportional.
C.He made a calculation error in the final step.
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.

Solution:

Step 1: Identify the relationship: x and y are directly proportional.

Step 2: Recall the formula for direct proportion: x1/y1 = x2/y2.

Step 3: Recall the formula for inverse proportion: x1y1 = x2y2. Rohan used the inverse proportion formula.

Step 4: Therefore, Rohan incorrectly assumed the relationship was inverse proportion instead of direct proportion. The correct setup for direct proportion would be 4/10 = 12/y.

5Which of the following statements is TRUE regarding two quantities, P and Q, that are inversely proportional?

A.As P increases, Q also increases proportionally.
B.The ratio P/Q remains constant.
C.The product P × Q remains constant.
D.Their difference P - Q remains constant.
Show Answer+

Answer: The product P × Q remains constant.

Hint: Think about how the values of two quantities change when they are inversely proportional to each other.

Solution:

Step 1: Understand inverse proportion. Two quantities are inversely proportional if an increase in one leads to a proportional decrease in the other, and vice versa.

Step 2: The defining characteristic of inverse proportion is that their product (P × Q) is always constant. This constant is called the constant of proportionality. — P × Q = k (where k is the constant of proportionality)

6Which of the following situations describes an inverse proportion?

A.The number of hours worked and the wages earned.
B.The area of a square and its side length.
C.The speed of a train and the time taken to cover a fixed distance.
D.The number of items bought and the total cost.
Show Answer+

Answer: The speed of a train and the time taken to cover a fixed distance.

Hint: For inverse proportion, as one quantity increases, the other should decrease proportionally.

Solution:

Step 1: Analyze each option. A) More hours worked, more wages earned (Direct). B) As side length increases, area increases (Not directly proportional, but not inverse). C) As the speed of a train increases, the time taken to cover a fixed distance decreases (Inverse). D) More items bought, higher total cost (Direct).

Step 2: Identify the scenario where an increase in one quantity leads to a proportional decrease in the other.

7A car takes 3 hours to travel a certain distance at a speed of 60 km/h. How much time will it take to travel the same distance at a speed of 90 km/h?

A.1 hour
B.2 hours
C.4 hours
D.4.5 hours
Show Answer+

Answer: 2 hours

Hint: Speed and time taken to cover a fixed distance are inversely proportional. Use the formula x1y1 = x2y2.

Solution:

Step 1: Identify the quantities: Speed (S) and Time (T). They are inversely proportional for a fixed distance. So, their product remains constant. — S1 × T1 = S2 × T2

Step 2: Given S1 = 60 km/h, T1 = 3 hours, S2 = 90 km/h. We need to find T2.

Step 3: Substitute the values: 60 × 3 = 90 × T2.

Step 4: Solve for T2: 180 = 90 × T2 => T2 = 180 / 90 = 2 hours.

8Consider the problem: '15 workers can build a wall in 48 hours. How many workers will be required to build the same wall in 30 hours?' Student A used (15/48) = (x/30). Student B used (15 × 48) = (x × 30). Which student chose the correct method and why?

A.Student A, because workers and time are directly proportional.
B.Student B, because workers and time are inversely proportional.
C.Student A, because the ratio of workers to time should be constant.
D.Both are incorrect; a different method is needed.
Show Answer+

Answer: Student B, because workers and time are inversely proportional.

Hint: Think about how the number of workers affects the time taken to complete a fixed amount of work.

Solution:

Step 1: Analyze the relationship between the number of workers and the time taken to build a wall. If you increase the number of workers, the time taken to build the same wall will decrease. This is an inverse proportion.

Step 2: Recall the formula for inverse proportion: x1y1 = x2y2.

Step 3: Student A used x1/y1 = x2/y2, which is for direct proportion. Student B used x1y1 = x2y2, which is for inverse proportion.

Step 4: Therefore, Student B chose the correct method because the number of workers and the time taken to complete a fixed job are inversely proportional.

9If a machine fills 420 bottles in 3 hours, then it will fill ______ bottles in 5 hours, assuming it works at a constant rate.

A.600
B.700
C.720
D.840
Show Answer+

Answer: 700

Hint: The number of bottles filled and the time taken are directly proportional.

Solution:

Step 1: Let B be the number of bottles and T be the time. Since the machine works at a constant rate, B and T are directly proportional: B1/T1 = B2/T2.

Step 2: Given B1 = 420 bottles, T1 = 3 hours, T2 = 5 hours. We need to find B2.

Step 3: Substitute the values: 420/3 = B2/5.

Step 4: Solve for B2: 140 = B2/5 => B2 = 140 × 5 = 700 bottles.

10A contractor estimates that 3 persons could rewire a house in 4 days. If he uses 4 persons instead of 3, how long should they take to complete the job?

A.2 days
B.2.5 days
C.3 days
D.5 days
Show Answer+

Answer: 3 days

Hint: The number of persons and the time taken to complete a fixed job are inversely proportional.

Solution:

Step 1: Let P be the number of persons and D be the number of days. They are inversely proportional: P1 × D1 = P2 × D2.

Step 2: Given P1 = 3 persons, D1 = 4 days, P2 = 4 persons. We need to find D2.

Step 3: Substitute the values: 3 × 4 = 4 × D2.

Step 4: Solve for D2: 12 = 4 × D2 => D2 = 12 / 4 = 3 days.

Want more questions?

Practice 60+ questions with AI-powered doubt clearing and step-by-step solutions.

Practice More

Tips for Variation (चलन) MCQs

  • 1Read each question carefully and identify what is being asked before looking at the options.
  • 2Try to solve the problem mentally or on paper first, then match your answer with the options.
  • 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
  • 4Check units, signs, and edge cases — these are common traps in Variation (चलन) MCQs.
  • 5Review your mistakes after completing the test to build lasting understanding.

Master Variation (चलन) on SparkEd

Go beyond MCQs. Practice at three difficulty levels with instant feedback, solutions, and an AI coach to clear every doubt.

Start Practising

SparkEd Maths offers free MCQ tests for Class 1-10 across 7 education boards. All questions are aligned to the 2025-26 syllabus with step-by-step solutions and AI-powered doubt clearing.