Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 94 · 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.₹90 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹90 (b) ₹45 (c) ₹15 (d) ₹75
2. 2.If 7 kites cost ₹147, how much do 4 kites cost? (a) ₹84 (b) ₹588 (c) ₹144 (d) ₹105
3. 3.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 7 days (d) 6 days
4. 4.If 6 kites cost ₹96, how much do 5 kites cost? (a) ₹95 (b) ₹96 (c) ₹80 (d) ₹480
5. 5.₹184 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹23 (b) ₹115 (c) ₹69 (d) ₹92
6. 6.₹500 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹250 (b) ₹500 (c) ₹50 (d) ₹450
7. 7.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 10 days (d) 9 days
8. 8.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 12 days (c) 11 days (d) 9 days
9. 9.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 43 days (b) 17 days (c) 42 days (d) 7 days
10. 10.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 1 day (c) 6 days (d) 8 days
11. 11.If 9 pens cost ₹81, how much do 6 pens cost? (a) ₹78 (b) ₹63 (c) ₹54 (d) ₹486
12. 12.₹280 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹280 (b) ₹140 (c) ₹35 (d) ₹245
13. 13.If 9 mangoes cost ₹180, how much do 3 mangoes cost? (a) ₹80 (b) ₹60 (c) ₹174 (d) ₹540
14. 14.If 9 mangoes cost ₹144, how much do 12 mangoes cost? (a) ₹208 (b) ₹192 (c) ₹147 (d) ₹1728
15. 15.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 32 days (c) 2 days (d) 17 days
16. 16.₹24 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹24 (b) ₹12 (c) ₹18 (d) ₹6
17. 17.₹168 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹24 (b) ₹84 (c) ₹48 (d) ₹120
18. 18.If 2 kites cost ₹30, how much do 7 kites cost? (a) ₹210 (b) ₹35 (c) ₹120 (d) ₹105
19. 19.If 4 mangoes cost ₹100, how much do 7 mangoes cost? (a) ₹700 (b) ₹103 (c) ₹200 (d) ₹175
20. 20.₹70 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹35 (b) ₹60 (c) ₹70 (d) ₹10
21. 21.If 9 kites cost ₹36, how much do 10 kites cost? (a) ₹360 (b) ₹40 (c) ₹44 (d) ₹37
22. 22.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 11 days (c) 26 days (d) 15 days
23. 23.₹147 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹105 (b) ₹42 (c) ₹126 (d) ₹21
24. 24.₹63 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹56 (b) ₹14 (c) ₹7 (d) ₹49
25. 25.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 12 days (d) 7 days
26. 26.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 5 days (d) 4 days
27. 27.If 9 kites cost ₹63, how much do 10 kites cost? (a) ₹77 (b) ₹64 (c) ₹630 (d) ₹70
28. 28.If 8 pens cost ₹56, how much do 12 pens cost? (a) ₹91 (b) ₹672 (c) ₹84 (d) ₹60
29. 29.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 5 days (d) 10 days
30. 30.₹64 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹64 (b) ₹32 (c) ₹8 (d) ₹56
31. 31.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 34 days (c) 33 days (d) 17 days
32. 32.₹360 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹200 (b) ₹160 (c) ₹180 (d) ₹40
33. 33.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 9 days (d) 13 days
34. 34.If 7 kites cost ₹49, how much do 3 kites cost? (a) ₹147 (b) ₹28 (c) ₹45 (d) ₹21
35. 35.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 13 days
36. 36.₹81 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹18 (b) ₹63 (c) ₹9 (d) ₹72
37. 37.If 2 mangoes cost ₹20, how much do 7 mangoes cost? (a) ₹140 (b) ₹25 (c) ₹80 (d) ₹70
38. 38.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 29 days (c) 3 days (d) 13 days
39. 39.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 19 days (d) 2 days
40. 40.If 3 pens cost ₹27, how much do 2 pens cost? (a) ₹27 (b) ₹54 (c) ₹18 (d) ₹26

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