Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 689 · 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.If 3 notebooks cost ₹51, how much do 12 notebooks cost? (a) ₹612 (b) ₹221 (c) ₹204 (d) ₹60
2. 2.If 2 mangoes cost ₹42, how much do 6 mangoes cost? (a) ₹46 (b) ₹147 (c) ₹252 (d) ₹126
3. 3.If 7 pens cost ₹35, how much do 5 pens cost? (a) ₹175 (b) ₹30 (c) ₹33 (d) ₹25
4. 4.If 2 pens cost ₹28, how much do 3 pens cost? (a) ₹56 (b) ₹42 (c) ₹29 (d) ₹84
5. 5.If 7 kites cost ₹112, how much do 11 kites cost? (a) ₹116 (b) ₹176 (c) ₹192 (d) ₹1232
6. 6.If 6 mangoes cost ₹102, how much do 2 mangoes cost? (a) ₹34 (b) ₹98 (c) ₹204 (d) ₹51
7. 7.₹108 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹36 (b) ₹72 (c) ₹108 (d) ₹54
8. 8.₹54 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹36 (b) ₹54 (c) ₹27 (d) ₹18
9. 9.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 2 days (d) 15 days
10. 10.₹168 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹21 (b) ₹84 (c) ₹63 (d) ₹105
11. 11.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 12 days (d) 9 days
12. 12.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 2 days (d) 4 days
13. 13.₹492 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹246 (b) ₹205 (c) ₹287 (d) ₹41
14. 14.₹532 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹266 (b) ₹38 (c) ₹342 (d) ₹190
15. 15.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 19 days (d) 4 days
16. 16.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 40 days (c) 16 days (d) 41 days
17. 17.₹162 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹90 (b) ₹72 (c) ₹18 (d) ₹81
18. 18.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 37 days (b) 3 days (c) 15 days (d) 36 days
19. 19.If 8 kites cost ₹40, how much do 7 kites cost? (a) ₹39 (b) ₹280 (c) ₹40 (d) ₹35
20. 20.₹98 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹14 (b) ₹49 (c) ₹84 (d) ₹98
21. 21.₹160 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹20 (b) ₹80 (c) ₹100 (d) ₹60
22. 22.₹104 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹64 (b) ₹52 (c) ₹40 (d) ₹8
23. 23.9 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 3 days (c) 17 days (d) 46 days
24. 24.If 8 notebooks cost ₹200, how much do 2 notebooks cost? (a) ₹75 (b) ₹50 (c) ₹400 (d) ₹194
25. 25.₹231 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹21 (b) ₹126 (c) ₹147 (d) ₹105
26. 26.If 2 mangoes cost ₹6, how much do 5 mangoes cost? (a) ₹15 (b) ₹18 (c) ₹30 (d) ₹9
27. 27.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 19 days (d) 49 days
28. 28.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 27 days (c) 28 days (d) 13 days
29. 29.If 3 pens cost ₹21, how much do 7 pens cost? (a) ₹25 (b) ₹49 (c) ₹56 (d) ₹147
30. 30.If 9 mangoes cost ₹216, how much do 5 mangoes cost? (a) ₹212 (b) ₹1080 (c) ₹120 (d) ₹144
31. 31.₹230 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹23 (b) ₹207 (c) ₹230 (d) ₹115
32. 32.₹156 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹78 (b) ₹13 (c) ₹65 (d) ₹91
33. 33.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 45 days (b) 21 days (c) 9 days (d) 5 days
34. 34.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 7 days (d) 6 days
35. 35.₹336 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹168 (b) ₹24 (c) ₹216 (d) ₹120
36. 36.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 9 days (d) 14 days
37. 37.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 12 days (c) 7 days (d) 13 days
38. 38.If 2 pens cost ₹44, how much do 10 pens cost? (a) ₹440 (b) ₹52 (c) ₹242 (d) ₹220
39. 39.If 4 mangoes cost ₹72, how much do 9 mangoes cost? (a) ₹180 (b) ₹77 (c) ₹648 (d) ₹162
40. 40.₹147 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹105 (b) ₹21 (c) ₹63 (d) ₹84

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