Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 616 · 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.₹343 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹343 (b) ₹295 (c) ₹49 (d) ₹294
2. 2.₹396 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹216 (b) ₹198 (c) ₹180 (d) ₹36
3. 3.If 6 mangoes cost ₹18, how much do 4 mangoes cost? (a) ₹12 (b) ₹15 (c) ₹72 (d) ₹16
4. 4.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 8 days (d) 9 days
5. 5.If 3 kites cost ₹48, how much do 12 kites cost? (a) ₹576 (b) ₹208 (c) ₹57 (d) ₹192
6. 6.If 5 mangoes cost ₹60, how much do 12 mangoes cost? (a) ₹67 (b) ₹720 (c) ₹144 (d) ₹156
7. 7.If 6 kites cost ₹54, how much do 8 kites cost? (a) ₹432 (b) ₹81 (c) ₹56 (d) ₹72
8. 8.₹119 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹17 (b) ₹103 (c) ₹102 (d) ₹119
9. 9.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 18 days (c) 19 days (d) 12 days
10. 10.₹378 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹189 (b) ₹42 (c) ₹378 (d) ₹336
11. 11.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 11 days
12. 12.₹450 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹135 (b) ₹225 (c) ₹45 (d) ₹315
13. 13.₹410 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹287 (b) ₹123 (c) ₹205 (d) ₹41
14. 14.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 3 days (d) 16 days
15. 15.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 9 days (c) 23 days (d) 13 days
16. 16.If 5 pens cost ₹30, how much do 2 pens cost? (a) ₹60 (b) ₹18 (c) ₹12 (d) ₹27
17. 17.If 9 kites cost ₹180, how much do 6 kites cost? (a) ₹120 (b) ₹1080 (c) ₹177 (d) ₹140
18. 18.If 6 notebooks cost ₹24, how much do 9 notebooks cost? (a) ₹40 (b) ₹216 (c) ₹36 (d) ₹27
19. 19.₹145 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹29 (b) ₹117 (c) ₹116 (d) ₹145
20. 20.If 8 mangoes cost ₹168, how much do 7 mangoes cost? (a) ₹168 (b) ₹1176 (c) ₹167 (d) ₹147
21. 21.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 18 days (c) 3 days (d) 4 days
22. 22.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 15 days (c) 27 days (d) 3 days
23. 23.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 48 days (c) 3 days (d) 6 days
24. 24.₹18 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹9 (b) ₹18 (c) ₹12 (d) ₹6
25. 25.₹539 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹98 (b) ₹490 (c) ₹441 (d) ₹49
26. 26.₹35 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹7 (b) ₹28 (c) ₹21 (d) ₹14
27. 27.₹364 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹224 (b) ₹28 (c) ₹140 (d) ₹182
28. 28.If 3 pens cost ₹42, how much do 2 pens cost? (a) ₹41 (b) ₹42 (c) ₹84 (d) ₹28
29. 29.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 14 days (d) 4 days
30. 30.₹121 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹99 (b) ₹11 (c) ₹88 (d) ₹33
31. 31.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 3 days (d) 1 day
32. 32.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 5 days (d) 4 days
33. 33.If 2 mangoes cost ₹8, how much do 4 mangoes cost? (a) ₹20 (b) ₹16 (c) ₹10 (d) ₹32
34. 34.If 5 mangoes cost ₹70, how much do 12 mangoes cost? (a) ₹182 (b) ₹168 (c) ₹77 (d) ₹840
35. 35.If 5 mangoes cost ₹110, how much do 2 mangoes cost? (a) ₹107 (b) ₹44 (c) ₹66 (d) ₹220
36. 36.If 2 notebooks cost ₹34, how much do 7 notebooks cost? (a) ₹119 (b) ₹136 (c) ₹39 (d) ₹238
37. 37.If 9 kites cost ₹27, how much do 6 kites cost? (a) ₹18 (b) ₹21 (c) ₹24 (d) ₹162
38. 38.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 19 days (c) 7 days (d) 40 days
39. 39.₹189 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹162 (b) ₹27 (c) ₹135 (d) ₹54
40. 40.If 5 mangoes cost ₹65, how much do 6 mangoes cost? (a) ₹66 (b) ₹390 (c) ₹78 (d) ₹91

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