Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 530 · 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. 1.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 7 days (d) 28 days
2. 2.If 3 mangoes cost ₹12, how much do 10 mangoes cost? (a) ₹19 (b) ₹120 (c) ₹44 (d) ₹40
3. 3.₹78 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹54 (b) ₹6 (c) ₹39 (d) ₹24
4. 4.If 4 notebooks cost ₹20, how much do 6 notebooks cost? (a) ₹22 (b) ₹120 (c) ₹35 (d) ₹30
5. 5.If 9 kites cost ₹144, how much do 8 kites cost? (a) ₹1152 (b) ₹144 (c) ₹143 (d) ₹128
6. 6.If 6 notebooks cost ₹126, how much do 10 notebooks cost? (a) ₹1260 (b) ₹210 (c) ₹130 (d) ₹231
7. 7.If 6 kites cost ₹132, how much do 12 kites cost? (a) ₹1584 (b) ₹286 (c) ₹264 (d) ₹138
8. 8.₹60 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹30 (b) ₹48 (c) ₹60 (d) ₹12
9. 9.₹300 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹125 (b) ₹175 (c) ₹25 (d) ₹150
10. 10.₹70 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹35 (b) ₹20 (c) ₹50 (d) ₹10
11. 11.If 9 mangoes cost ₹180, how much do 12 mangoes cost? (a) ₹260 (b) ₹183 (c) ₹2160 (d) ₹240
12. 12.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 13 days (c) 20 days (d) 7 days
13. 13.₹279 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹31 (b) ₹155 (c) ₹124 (d) ₹186
14. 14.If 9 pens cost ₹135, how much do 4 pens cost? (a) ₹540 (b) ₹130 (c) ₹60 (d) ₹75
15. 15.If 8 pens cost ₹72, how much do 9 pens cost? (a) ₹648 (b) ₹73 (c) ₹90 (d) ₹81
16. 16.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 26 days (c) 11 days (d) 27 days
17. 17.₹132 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹72 (b) ₹12 (c) ₹66 (d) ₹60
18. 18.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 17 days (d) 4 days
19. 19.If 8 pens cost ₹48, how much do 2 pens cost? (a) ₹42 (b) ₹96 (c) ₹18 (d) ₹12
20. 20.₹324 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹27 (b) ₹162 (c) ₹189 (d) ₹135
21. 21.If 8 notebooks cost ₹72, how much do 2 notebooks cost? (a) ₹66 (b) ₹27 (c) ₹144 (d) ₹18
22. 22.₹98 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹49 (b) ₹28 (c) ₹14 (d) ₹70
23. 23.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 35 days (c) 17 days (d) 11 days
24. 24.₹440 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹320 (b) ₹120 (c) ₹220 (d) ₹40
25. 25.₹287 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹41 (b) ₹205 (c) ₹123 (d) ₹164
26. 26.₹275 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹125 (b) ₹150 (c) ₹175 (d) ₹25
27. 27.₹99 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹89 (b) ₹99 (c) ₹11 (d) ₹88
28. 28.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 11 days (c) 14 days (d) 16 days
29. 29.₹156 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹65 (b) ₹91 (c) ₹78 (d) ₹13
30. 30.If 4 mangoes cost ₹56, how much do 2 mangoes cost? (a) ₹42 (b) ₹112 (c) ₹28 (d) ₹54
31. 31.₹162 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹81 (b) ₹36 (c) ₹126 (d) ₹18
32. 32.If 5 pens cost ₹115, how much do 9 pens cost? (a) ₹230 (b) ₹207 (c) ₹119 (d) ₹1035
33. 33.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹84 (b) ₹12 (c) ₹60 (d) ₹108
34. 34.If 7 notebooks cost ₹21, how much do 3 notebooks cost? (a) ₹12 (b) ₹9 (c) ₹17 (d) ₹63
35. 35.₹434 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹155 (b) ₹217 (c) ₹31 (d) ₹279
36. 36.5 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 21 days (d) 20 days
37. 37.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 28 days (b) 10 days (c) 7 days (d) 18 days
38. 38.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 4 days (d) 9 days
39. 39.If 9 kites cost ₹36, how much do 5 kites cost? (a) ₹32 (b) ₹24 (c) ₹180 (d) ₹20
40. 40.₹105 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹35 (b) ₹105 (c) ₹71 (d) ₹70

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