Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 77 · 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 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 17 days (d) 6 days
2. 2.₹132 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹132 (b) ₹110 (c) ₹22 (d) ₹66
3. 3.₹224 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹64 (b) ₹160 (c) ₹112 (d) ₹32
4. 4.If 8 pens cost ₹88, how much do 4 pens cost? (a) ₹44 (b) ₹352 (c) ₹84 (d) ₹55
5. 5.If 8 notebooks cost ₹24, how much do 12 notebooks cost? (a) ₹28 (b) ₹39 (c) ₹288 (d) ₹36
6. 6.If 8 mangoes cost ₹104, how much do 9 mangoes cost? (a) ₹130 (b) ₹936 (c) ₹117 (d) ₹105
7. 7.If 9 kites cost ₹189, how much do 10 kites cost? (a) ₹231 (b) ₹1890 (c) ₹210 (d) ₹190
8. 8.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 7 days (d) 9 days
9. 9.If 6 notebooks cost ₹96, how much do 12 notebooks cost? (a) ₹208 (b) ₹1152 (c) ₹192 (d) ₹102
10. 10.₹370 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹111 (b) ₹259 (c) ₹185 (d) ₹37
11. 11.7 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) 6 days (d) 13 days
12. 12.₹350 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹35 (b) ₹315 (c) ₹175 (d) ₹350
13. 13.₹224 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹16 (b) ₹144 (c) ₹80 (d) ₹112
14. 14.₹572 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹286 (b) ₹176 (c) ₹44 (d) ₹396
15. 15.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 5 days (c) 9 days (d) 15 days
16. 16.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 5 days (d) 9 days
17. 17.₹272 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹34 (b) ₹136 (c) ₹272 (d) ₹238
18. 18.If 7 kites cost ₹91, how much do 6 kites cost? (a) ₹90 (b) ₹78 (c) ₹546 (d) ₹91
19. 19.₹490 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹245 (b) ₹343 (c) ₹49 (d) ₹147
20. 20.If 7 mangoes cost ₹63, how much do 12 mangoes cost? (a) ₹108 (b) ₹117 (c) ₹756 (d) ₹68
21. 21.If 2 mangoes cost ₹40, how much do 4 mangoes cost? (a) ₹80 (b) ₹160 (c) ₹100 (d) ₹42
22. 22.If 6 notebooks cost ₹150, how much do 7 notebooks cost? (a) ₹1050 (b) ₹175 (c) ₹151 (d) ₹200
23. 23.If 2 mangoes cost ₹46, how much do 10 mangoes cost? (a) ₹230 (b) ₹460 (c) ₹253 (d) ₹54
24. 24.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 18 days (c) 4 days (d) 36 days
25. 25.₹45 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹30 (b) ₹5 (c) ₹20 (d) ₹25
26. 26.If 4 pens cost ₹64, how much do 2 pens cost? (a) ₹62 (b) ₹32 (c) ₹128 (d) ₹48
27. 27.If 4 kites cost ₹48, how much do 9 kites cost? (a) ₹432 (b) ₹108 (c) ₹53 (d) ₹120
28. 28.If 6 pens cost ₹54, how much do 11 pens cost? (a) ₹59 (b) ₹594 (c) ₹108 (d) ₹99
29. 29.₹63 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹63 (b) ₹56 (c) ₹7 (d) ₹57
30. 30.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 36 days (b) 4 days (c) 18 days (d) 6 days
31. 31.₹517 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹235 (b) ₹47 (c) ₹282 (d) ₹329
32. 32.₹686 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹245 (b) ₹343 (c) ₹49 (d) ₹441
33. 33.If 3 kites cost ₹12, how much do 12 kites cost? (a) ₹144 (b) ₹48 (c) ₹52 (d) ₹21
34. 34.If 6 pens cost ₹150, how much do 11 pens cost? (a) ₹275 (b) ₹155 (c) ₹1650 (d) ₹300
35. 35.If 9 mangoes cost ₹162, how much do 11 mangoes cost? (a) ₹216 (b) ₹198 (c) ₹164 (d) ₹1782
36. 36.₹145 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹117 (b) ₹145 (c) ₹116 (d) ₹29
37. 37.If 2 notebooks cost ₹42, how much do 11 notebooks cost? (a) ₹231 (b) ₹51 (c) ₹462 (d) ₹252
38. 38.₹70 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹60 (b) ₹70 (c) ₹10 (d) ₹35
39. 39.₹234 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹117 (b) ₹195 (c) ₹234 (d) ₹39
40. 40.₹180 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹90 (b) ₹72 (c) ₹36 (d) ₹108

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