Chapter Exam

Chapter-7 Proportional Reasoning — Online MCQ Test

Q: If x and y are in direct proportion and x = 4 when y = 8, what is the constant of proportionality?

Answer: B. 2 — In direct proportion, y = kx, so k = y/x = 8/4 = 2.

Q: Which of the following represents an inverse proportion?

Answer: C. xy = 10 — In inverse proportion, the product of two variables is constant (xy = k), which is represented by xy = 10.

Q: If 5 pens cost Rs. 50, what is the cost of 8 pens using the unitary method?

Answer: B. Rs. 80 — Cost of 1 pen = 50/5 = Rs. 10. Cost of 8 pens = 10 × 8 = Rs. 80.

Q: What is the ratio of 12 to 18 in its simplest form?

Answer: A. 2:3 — Dividing both 12 and 18 by their GCD (6) gives 12:18 = 2:3.

Q: If y is inversely proportional to x and y = 24 when x = 3, find y when x = 8.

Answer: A. 9 — In inverse proportion, xy = k. So k = 3 × 24 = 72. When x = 8, y = 72/8 = 9.

Q: A recipe requires 2 cups of flour for 3 servings. How much flour is needed for 9 servings?

Answer: B. 6 cups — Using unitary method: flour for 1 serving = 2/3 cups. For 9 servings = (2/3) × 9 = 6 cups.

Q: If p and q are inversely proportional, and p = 6 when q = 8, find q when p = 12.

Answer: B. 4 — In inverse proportion, pq = k. So k = 6 × 8 = 48. When p = 12, q = 48/12 = 4.

Q: The price of 15 meters of cloth is Rs. 750. A tailor needs 4 meters for a shirt and 6 meters for a dress. What is the total cost of cloth for both?

Answer: D. Rs. 500 — Cost per meter = 750/15 = Rs. 50. Total cloth needed = 4 + 6 = 10 meters. Total cost = 50 × 10 = Rs. 500.

Q: If the ratio of A to B is 3:4 and the ratio of B to C is 5:6, find the ratio A:B:C. (Pro level)

Answer: A. 15:20:24 — A:B = 3:4 and B:C = 5:6. To combine, make B equal: A:B = (3×5):(4×5) = 15:20 and B:C = (5×4):(6×4) = 20:24. Thus A:B:C = 15:20:24.

Q: The price of petrol increases by 10% and then decreases by 10%. What is the net change in price? (Pro level)

Answer: B. 1% decrease — Let original price = 100. After 10% increase = 110. After 10% decrease = 110 × 0.9 = 99. Net change = 99 - 100 = -1, which is 1% decrease.

MATHS · Grade 8 · CBSE(NCERT)

Practice Chapter-7 Proportional Reasoning with a free chapter-wise online MCQ test for CBSE(NCERT) Grade 8 MATHS. This chapter covers: direct proportion - inverse proportion - unitary method - constant of variation - ratios - comparing quantities. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter-7 Proportional Reasoning — Important Questions & Answers (FAQ)

Frequently asked questions from CBSE(NCERT) Grade 8 MATHS — Chapter-7 Proportional Reasoning, with answers and explanations. These are sample questions; the exam has its own separate question set.

If x and y are in direct proportion and x = 4 when y = 8, what is the constant of proportionality?

A. 0.5
B. 2 ✓
C. 4
D. 8

Answer: B. 2
In direct proportion, y = kx, so k = y/x = 8/4 = 2.

Which of the following represents an inverse proportion?

A. y = 2x
B. y = x/2
C. xy = 10 ✓
D. x + y = 10

Answer: C. xy = 10
In inverse proportion, the product of two variables is constant (xy = k), which is represented by xy = 10.

If 5 pens cost Rs. 50, what is the cost of 8 pens using the unitary method?

A. Rs. 70
B. Rs. 80 ✓
C. Rs. 90
D. Rs. 100

Answer: B. Rs. 80
Cost of 1 pen = 50/5 = Rs. 10. Cost of 8 pens = 10 × 8 = Rs. 80.

What is the ratio of 12 to 18 in its simplest form?

A. 2:3 ✓
B. 3:2
C. 4:6
D. 6:9

Answer: A. 2:3
Dividing both 12 and 18 by their GCD (6) gives 12:18 = 2:3.

If y is inversely proportional to x and y = 24 when x = 3, find y when x = 8.

A. 9 ✓
B. 64
C. 12
D. 72

Answer: A. 9
In inverse proportion, xy = k. So k = 3 × 24 = 72. When x = 8, y = 72/8 = 9.

A recipe requires 2 cups of flour for 3 servings. How much flour is needed for 9 servings?

A. 4 cups
B. 6 cups ✓
C. 8 cups
D. 5 cups

Answer: B. 6 cups
Using unitary method: flour for 1 serving = 2/3 cups. For 9 servings = (2/3) × 9 = 6 cups.

If p and q are inversely proportional, and p = 6 when q = 8, find q when p = 12.

A. 2
B. 4 ✓
C. 16
D. 24

Answer: B. 4
In inverse proportion, pq = k. So k = 6 × 8 = 48. When p = 12, q = 48/12 = 4.

The price of 15 meters of cloth is Rs. 750. A tailor needs 4 meters for a shirt and 6 meters for a dress. What is the total cost of cloth for both?

A. Rs. 200
B. Rs. 300
C. Rs. 400
D. Rs. 500 ✓

Answer: D. Rs. 500
Cost per meter = 750/15 = Rs. 50. Total cloth needed = 4 + 6 = 10 meters. Total cost = 50 × 10 = Rs. 500.

If the ratio of A to B is 3:4 and the ratio of B to C is 5:6, find the ratio A:B:C. (Pro level)

A. 15:20:24 ✓
B. 10:15:18
C. 5:8:12
D. 6:8:10

Answer: A. 15:20:24
A:B = 3:4 and B:C = 5:6. To combine, make B equal: A:B = (3×5):(4×5) = 15:20 and B:C = (5×4):(6×4) = 20:24. Thus A:B:C = 15:20:24.

The price of petrol increases by 10% and then decreases by 10%. What is the net change in price? (Pro level)

A. No change
B. 1% decrease ✓
C. 1% increase
D. 5% decrease

Answer: B. 1% decrease
Let original price = 100. After 10% increase = 110. After 10% decrease = 110 × 0.9 = 99. Net change = 99 - 100 = -1, which is 1% decrease.

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