Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 481 · 40 questions

How to solve it (Go through one): Unitary: cost of one = total ÷ number; then multiply by how many you need. Ratio p : q of a total: one part = total ÷ (p + q); a share = its parts × one part. Workers and days go the opposite way: total work = workers × days; days = total work ÷ new number of workers.

1. 1.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 2 days (d) 3 days
2. 2.₹374 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹102 (b) ₹187 (c) ₹272 (d) ₹34
3. 3.₹290 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹290 (b) ₹29 (c) ₹261 (d) ₹145
4. 4.₹279 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹31 (b) ₹248 (c) ₹279 (d) ₹249
5. 5.₹28 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹14 (b) ₹28 (c) ₹7 (d) ₹21
6. 6.If 4 pens cost ₹32, how much do 5 pens cost? (a) ₹160 (b) ₹48 (c) ₹40 (d) ₹33
7. 7.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 34 days (b) 15 days (c) 33 days (d) 7 days
8. 8.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 49 days (d) 19 days
9. 9.₹208 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹104 (b) ₹16 (c) ₹64 (d) ₹144
10. 10.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 1 day (d) 10 days
11. 11.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 12 days (d) 2 days
12. 12.₹175 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹25 (b) ₹150 (c) ₹125 (d) ₹50
13. 13.₹102 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹17 (b) ₹85 (c) ₹51 (d) ₹102
14. 14.₹209 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹152 (b) ₹57 (c) ₹171 (d) ₹19
15. 15.₹189 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹108 (b) ₹81 (c) ₹135 (d) ₹27
16. 16.If 4 mangoes cost ₹100, how much do 9 mangoes cost? (a) ₹225 (b) ₹250 (c) ₹900 (d) ₹105
17. 17.If 4 pens cost ₹60, how much do 3 pens cost? (a) ₹180 (b) ₹60 (c) ₹45 (d) ₹59
18. 18.₹288 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹288 (b) ₹32 (c) ₹144 (d) ₹256
19. 19.₹81 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹55 (b) ₹27 (c) ₹81 (d) ₹54
20. 20.₹423 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹188 (b) ₹47 (c) ₹282 (d) ₹235
21. 21.₹187 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹17 (b) ₹34 (c) ₹170 (d) ₹153
22. 22.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 28 days (d) 15 days
23. 23.₹637 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹392 (b) ₹49 (c) ₹245 (d) ₹441
24. 24.If 4 mangoes cost ₹16, how much do 10 mangoes cost? (a) ₹22 (b) ₹40 (c) ₹160 (d) ₹44
25. 25.If 4 pens cost ₹68, how much do 6 pens cost? (a) ₹119 (b) ₹408 (c) ₹102 (d) ₹70
26. 26.₹30 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹30 (b) ₹24 (c) ₹15 (d) ₹6
27. 27.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 12 days (d) 18 days
28. 28.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 13 days (b) 8 days (c) 9 days (d) 10 days
29. 29.If 6 pens cost ₹90, how much do 2 pens cost? (a) ₹86 (b) ₹30 (c) ₹45 (d) ₹180
30. 30.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 2 days (c) 15 days (d) 14 days
31. 31.If 6 kites cost ₹96, how much do 4 kites cost? (a) ₹384 (b) ₹94 (c) ₹64 (d) ₹80
32. 32.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 13 days (c) 7 days (d) 4 days
33. 33.₹220 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹220 (b) ₹176 (c) ₹44 (d) ₹110
34. 34.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 4 days (d) 2 days
35. 35.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 11 days (d) 28 days
36. 36.₹315 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹210 (b) ₹35 (c) ₹175 (d) ₹140
37. 37.₹132 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹60 (b) ₹72 (c) ₹12 (d) ₹66
38. 38.If 9 notebooks cost ₹225, how much do 10 notebooks cost? (a) ₹226 (b) ₹2250 (c) ₹250 (d) ₹275
39. 39.₹66 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹36 (b) ₹6 (c) ₹33 (d) ₹30
40. 40.If 3 notebooks cost ₹18, how much do 10 notebooks cost? (a) ₹25 (b) ₹180 (c) ₹60 (d) ₹66

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