Ratio, Proportion & Percentages

46 Class 6 IMO Mathematics Olympiad practice questions on ratio, proportion & percentages, part of the Arithmetic topic area. Every question below includes the correct answer and a full explanation.

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1. What is 10% of 150?
- A.10
- B.12
- C.15
- D.20
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Answer: C. 15
10% of 150 = 150 ÷ 10 = 15.
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2. What is 25% of 240?
- A.50
- B.55
- C.60
- D.65
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Answer: C. 60
240 × 0.25 = 60.
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3. A shirt costs ₹800. It is sold at a discount of 15%. What is the selling price?
- A.₹660
- B.₹680
- C.₹700
- D.₹720
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Answer: B. ₹680
15% of 800 = 120. 800 − 120 = 680.
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4. Express the ratio 15:20 in simplest form.
- A.3:4
- B.4:5
- C.5:6
- D.2:3
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Answer: A. 3:4
Dividing both terms by their HCF, 5: 15÷5=3, 20÷5=4, giving 3:4.
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5. The ratio of boys to girls in a class is 3:2. If there are 18 boys, how many girls are there?
- A.10
- B.12
- C.14
- D.16
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Answer: B. 12
18 boys = 3 parts, so 1 part = 6. Girls = 2 parts = 12.
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6. What is 40% of 250?
- A.80
- B.90
- C.100
- D.110
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Answer: C. 100
250 × 0.40 = 100.
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7. In the ratio 1:4, what percentage of the total does the first part represent?
- A.15%
- B.20%
- C.25%
- D.40%
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Answer: B. 20%
Total parts = 1+4 = 5. First part = 1/5 = 20%.
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8. If 3 pens cost ₹45, what is the ratio of the cost of 1 pen to the cost of 5 pens?
- A.1:3
- B.1:4
- C.1:5
- D.1:6
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Answer: C. 1:5
1 pen costs ₹15, and 5 pens cost ₹75. The ratio 15:75 simplifies to 1:5.
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9. What is 75% of 160?
- A.100
- B.110
- C.120
- D.130
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Answer: C. 120
160 × 0.75 = 120.
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10. What percentage of 80 is 20?
- A.20%
- B.25%
- C.30%
- D.40%
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Answer: B. 25%
20/80 × 100 = 25%.
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11. Write 40% as a decimal.
- A.0.45
- B.0.4
- C.0.35
- D.0.5
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Answer: B. 0.4
40% = 40 ÷ 100 = 0.4.
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12. What is 20% of 120?
- A.34
- B.24
- C.14
- D.44
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Answer: B. 24
120 × 20 ÷ 100 = 24.
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13. What is 30% of 80?
- A.14
- B.44
- C.24
- D.34
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Answer: C. 24
80 × 30 ÷ 100 = 24.
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14. What is 25% of 400?
- A.90
- B.100
- C.120
- D.110
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Answer: B. 100
400 × 25 ÷ 100 = 100.
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15. What is the ratio of 6 to 8?
- A.6:14
- B.14:8
- C.6:8
- D.8:6
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Answer: C. 6:8
The ratio of 6 to 8 is written 6:8.
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16. What is 30% of 160?
- A.58
- B.38
- C.68
- D.48
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Answer: D. 48
160 × 30 ÷ 100 = 48.
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17. What is the ratio of 3 to 9?
- A.3:12
- B.3:9
- C.12:9
- D.9:3
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Answer: B. 3:9
The ratio of 3 to 9 is written 3:9.
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18. What is 25% of 80?
- A.40
- B.20
- C.10
- D.30
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Answer: B. 20
80 × 25 ÷ 100 = 20.
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19. What is the ratio of 2 to 6?
- A.2:6
- B.2:8
- C.8:6
- D.6:2
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Answer: A. 2:6
The ratio of 2 to 6 is written 2:6.
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20. A number increased by 20% becomes 60. What is the original number?
- A.40
- B.45
- C.48
- D.50
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Answer: D. 50
1.2x = 60, so x = 50.
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21. A shopkeeper bought a toy for ₹200 and sold it for ₹250. What is the profit percentage?
- A.20%
- B.25%
- C.30%
- D.50%
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Answer: B. 25%
Profit = ₹50. Profit% = 50/200 × 100 = 25%.
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22. The price of a book was reduced from ₹80 to ₹68. What is the percentage decrease?
- A.10%
- B.12%
- C.15%
- D.20%
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Answer: C. 15%
Decrease = ₹12. Percentage decrease = 12/80 × 100 = 15%.
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23. A mixture contains milk and water in the ratio 5:1. If there are 30 litres of milk, how much water is there?
- A.4
- B.5
- C.6
- D.8
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Answer: C. 6
30 litres = 5 parts, so 1 part = 6 litres, which is the amount of water.
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24. A number is decreased by 25% to give 60. What was the original number?
- A.70
- B.75
- C.80
- D.85
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Answer: C. 80
0.75x = 60, so x = 80.
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25. Two numbers are in the ratio 4:7. If their sum is 66, find the smaller number.
- A.22
- B.24
- C.26
- D.28
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Answer: B. 24
Total parts = 11, so 1 part = 6. Smaller number = 4 parts = 24.
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26. Write 10% as a decimal.
- A.0.2
- B.0.05
- C.0.15
- D.0.1
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Answer: D. 0.1
10% = 10 ÷ 100 = 0.1.
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27. Write 25% as a decimal.
- A.0.3
- B.0.25
- C.0.35
- D.0.2
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Answer: B. 0.25
25% = 25 ÷ 100 = 0.25.
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28. Write 60% as a decimal.
- A.0.55
- B.0.65
- C.0.7
- D.0.6
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Answer: D. 0.6
60% = 60 ÷ 100 = 0.6.
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29. What is the ratio of 2 to 9?
- A.11:9
- B.2:11
- C.2:9
- D.9:2
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Answer: C. 2:9
The ratio of 2 to 9 is written 2:9.
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30. What is 40% of 160?
- A.64
- B.74
- C.54
- D.84
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Answer: A. 64
160 × 40 ÷ 100 = 64.
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31. What is 40% of 80?
- A.22
- B.52
- C.32
- D.42
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Answer: C. 32
80 × 40 ÷ 100 = 32.
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32. What is the ratio of 4 to 6?
- A.4:6
- B.6:4
- C.4:10
- D.10:6
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Answer: A. 4:6
The ratio of 4 to 6 is written 4:6.
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33. What is the ratio of 9 to 8?
- A.9:17
- B.8:9
- C.17:8
- D.9:8
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Answer: D. 9:8
The ratio of 9 to 8 is written 9:8.
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34. What is 30% of 120?
- A.26
- B.36
- C.56
- D.46
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Answer: B. 36
120 × 30 ÷ 100 = 36.
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35. What is 30% of 200?
- A.50
- B.80
- C.70
- D.60
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Answer: D. 60
200 × 30 ÷ 100 = 60.
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36. What is 10% of 80?
- A.28
- B.-2
- C.8
- D.18
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Answer: C. 8
80 × 10 ÷ 100 = 8.
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37. Write 75% as a decimal.
- A.0.7
- B.0.8
- C.0.85
- D.0.75
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Answer: D. 0.75
75% = 75 ÷ 100 = 0.75.
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38. What is the ratio of 7 to 6?
- A.7:13
- B.6:7
- C.7:6
- D.13:6
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Answer: C. 7:6
The ratio of 7 to 6 is written 7:6.
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39. What is 10% of 160?
- A.36
- B.26
- C.6
- D.16
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Answer: D. 16
160 × 10 ÷ 100 = 16.
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40. What is the ratio of 4 to 3?
- A.4:7
- B.7:3
- C.3:4
- D.4:3
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Answer: D. 4:3
The ratio of 4 to 3 is written 4:3.
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41. What is the ratio of 9 to 7?
- A.9:7
- B.7:9
- C.9:16
- D.16:7
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Answer: A. 9:7
The ratio of 9 to 7 is written 9:7.
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42. What is 10% of 120?
- A.22
- B.2
- C.32
- D.12
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Answer: D. 12
120 × 10 ÷ 100 = 12.
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43. What is the ratio of 4 to 8?
- A.8:4
- B.4:12
- C.12:8
- D.4:8
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Answer: D. 4:8
The ratio of 4 to 8 is written 4:8.
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44. What is the ratio of 7 to 4?
- A.4:7
- B.11:4
- C.7:4
- D.7:11
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Answer: C. 7:4
The ratio of 7 to 4 is written 7:4.
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45. What is the ratio of 8 to 7?
- A.7:8
- B.8:7
- C.15:7
- D.8:15
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Answer: B. 8:7
The ratio of 8 to 7 is written 8:7.
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46. What is the ratio of 5 to 8?
- A.5:13
- B.8:5
- C.13:8
- D.5:8
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Answer: D. 5:8
The ratio of 5 to 8 is written 5:8.
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