Chapter 7: Ratio and Proportion - Mock Test
Instructions
- •This test has 20 questions covering all topics from Chapter 7
- •Questions are arranged as per CBSE paper pattern
- •Section A: 8 questions × 1 mark = 8 marks
- •Section B: 8 questions × 2 marks = 16 marks
- •Section C: 4 questions × 4 marks = 16 marks
- •No negative marking
- •Show all steps in your calculations
- •You can take this test multiple times
Mock Test Questions
Section A: 1 Mark Questions (8 × 1 = 8 marks)
1. Simplify the ratio 45:60 to its lowest terms.
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Answer: 3:4
2. If 6 pens cost Rs. 90, what is the cost of 1 pen?
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Answer: Rs. 15 (using unitary method: 90÷6)
3. Are the ratios 2:5 and 4:10 equal?
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Answer: Yes (Cross-multiply: 2×10 = 20, 5×4 = 20)
4. If speed increases, what happens to distance in the same time?
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Answer: Distance increases (direct variation)
5. What is the ratio of 2 hours to 120 minutes in simplest form?
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Answer: 1:1 (2 hours = 120 minutes)
6. In the proportion 5:x = 10:20, find x.
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Answer: x = 10 (Cross-multiply: 5×20 = 10×x)
7. If xy = 18 (constant), find y when x = 2.
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Answer: y = 9 (18÷2, indirect variation)
8. Divide 160 in ratio 3:5. First part is:
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Answer: Rs. 60 (3/8 × 160)
Section B: 2 Mark Questions (8 × 2 = 16 marks)
9. Divide Rs. 300 in ratio 2:3. Find each part.
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Answer: Total parts = 5. First = (2/5)×300 = Rs. 120. Second = (3/5)×300 = Rs. 180
10. If 8 workers build a wall in 9 days, in how many days will 12 workers build it?
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Answer: Total work = 8×9 = 72 worker-days. Days for 12 workers = 72÷12 = 6 days
11. Check whether 15:20 and 21:28 form a proportion. Show working.
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Answer: 15:20 = 3:4 (÷5). 21:28 = 3:4 (÷7). Yes, both equal 3:4, so they form proportion.
12. If y = 4x, find y when x = 5 and x = 10. Verify direct variation.
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Answer: When x=5: y=20. When x=10: y=40. Ratio y/x = 20/5 = 40/10 = 4 (constant) ✓
13. A car travels 240 km in 4 hours. Using unitary method, find distance in 6 hours at same speed.
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Answer: Distance in 1 hour = 240÷4 = 60 km. Distance in 6 hours = 60×6 = 360 km
14. Find x if (x+3):(x-1) = 5:3. Show all steps.
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Answer: Cross-multiply: 3(x+3) = 5(x-1) → 3x+9 = 5x-5 → 14 = 2x → x = 7
15. In a class, boys:girls = 4:3. If there are 28 students total, find number of boys.
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Answer: Total parts = 7. Boys = (4/7)×28 = 16 students
16. If xy = 24 (indirect variation), find y when x = 4 and when x = 6.
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Answer: When x=4: y=6. When x=6: y=4. As x increases, y decreases (inverse) ✓
Section C: 4 Mark Questions (4 × 4 = 16 marks)
17. Three friends divide a profit of Rs. 4500 in ratio 2:3:4. Find each person's share.
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Answer: Total parts = 2+3+4 = 9 First friend = (2/9)×4500 = Rs. 1000 Second friend = (3/9)×4500 = Rs. 1500 Third friend = (4/9)×4500 = Rs. 2000 Verification: 1000+1500+2000 = 4500 ✓
18. A mixture has milk and water in ratio 7:3. Total mixture is 50 liters. Find quantity of milk and water separately.
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Answer: Total parts = 7+3 = 10 Milk = (7/10)×50 = 35 liters Water = (3/10)×50 = 15 liters Check: 35+15 = 50 ✓
19. A shop sells oranges at Rs. 8 per orange. How many oranges can you buy with Rs. 240? Use unitary method.
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Answer: Cost per orange = Rs. 8 Number of oranges = 240÷8 = 30 oranges Or: 1 orange costs Rs. 8, so 240 will buy 240/8 = 30 oranges
20. If 10 machines produce 500 items in 5 days, how many days will 5 machines take to produce 500 items?
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Answer: Total machine-days = 10×5 = 50 For 500 items with 5 machines: Days = 50÷5 = 10 days Or: Half machines need double time: 5→10 days
Marking Scheme & Evaluation
Section A (1 Mark)
1 mark for correct answer. No partial marking.
Section B (2 Marks)
- • Correct answer with working: 2 marks
- • Correct method but minor error: 1 mark
- • Wrong answer without working: 0 marks
Section C (4 Marks)
- • Correct answer with all steps: 4 marks
- • Correct approach but minor error: 3 marks
- • Partially correct (≥50%): 2 marks
- • Some relevant working: 1 mark
- • No attempt or completely wrong: 0 marks
Performance Analysis
36-40 marks: Excellent! You have mastered the chapter.
30-35 marks: Very Good! You have strong understanding of ratios and proportions.
24-29 marks: Good! Practice more to strengthen concepts.
18-23 marks: Average. Review unitary method and variation concepts.
Below 18 marks: Need improvement. Study basics of ratio and proportion again.
Exam Preparation Tips
- ✓Always simplify ratios to lowest terms by dividing by HCF
- ✓Use cross-multiplication to check proportions or find unknowns
- ✓Always identify whether variation is direct (y=kx) or indirect (xy=k)
- ✓In unitary method, always find unit value first
- ✓Convert quantities to same units before making ratios