Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 663 · 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 7 pens cost ₹21, how much do 9 pens cost? (a) ₹189 (b) ₹27 (c) ₹23 (d) ₹30
2. 2.If 5 pens cost ₹120, how much do 4 pens cost? (a) ₹119 (b) ₹480 (c) ₹96 (d) ₹120
3. 3.₹559 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹43 (b) ₹430 (c) ₹387 (d) ₹172
4. 4.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 18 days (d) 3 days
5. 5.₹153 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹137 (b) ₹153 (c) ₹136 (d) ₹17
6. 6.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 4 days (d) 15 days
7. 7.If 6 pens cost ₹120, how much do 9 pens cost? (a) ₹123 (b) ₹200 (c) ₹180 (d) ₹1080
8. 8.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 1 day (d) 11 days
9. 9.₹329 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹47 (b) ₹94 (c) ₹235 (d) ₹282
10. 10.8 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 8 days (b) 18 days (c) 16 days (d) 9 days
11. 11.₹520 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹260 (b) ₹320 (c) ₹40 (d) ₹200
12. 12.If 7 kites cost ₹119, how much do 12 kites cost? (a) ₹1428 (b) ₹204 (c) ₹124 (d) ₹221
13. 13.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 9 days (d) 8 days
14. 14.If 8 kites cost ₹168, how much do 3 kites cost? (a) ₹163 (b) ₹84 (c) ₹63 (d) ₹504
15. 15.₹410 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹41 (b) ₹369 (c) ₹410 (d) ₹205
16. 16.If 5 pens cost ₹25, how much do 3 pens cost? (a) ₹20 (b) ₹23 (c) ₹15 (d) ₹75
17. 17.₹105 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹90 (b) ₹75 (c) ₹30 (d) ₹15
18. 18.₹190 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹95 (b) ₹171 (c) ₹19 (d) ₹190
19. 19.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 4 days (d) 10 days
20. 20.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 18 days (c) 2 days (d) 19 days
21. 21.If 2 kites cost ₹16, how much do 4 kites cost? (a) ₹32 (b) ₹40 (c) ₹64 (d) ₹18
22. 22.₹470 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹47 (b) ₹235 (c) ₹329 (d) ₹141
23. 23.If 7 kites cost ₹28, how much do 8 kites cost? (a) ₹32 (b) ₹224 (c) ₹29 (d) ₹36
24. 24.If 3 notebooks cost ₹9, how much do 4 notebooks cost? (a) ₹36 (b) ₹12 (c) ₹10 (d) ₹15
25. 25.₹572 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹176 (b) ₹44 (c) ₹396 (d) ₹286
26. 26.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 7 days (c) 23 days (d) 22 days
27. 27.₹484 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹44 (b) ₹242 (c) ₹264 (d) ₹220
28. 28.4 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
29. 29.If 4 mangoes cost ₹28, how much do 8 mangoes cost? (a) ₹63 (b) ₹32 (c) ₹224 (d) ₹56
30. 30.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 9 days
31. 31.If 5 kites cost ₹70, how much do 4 kites cost? (a) ₹280 (b) ₹56 (c) ₹69 (d) ₹70
32. 32.If 6 notebooks cost ₹54, how much do 10 notebooks cost? (a) ₹99 (b) ₹540 (c) ₹58 (d) ₹90
33. 33.If 2 kites cost ₹38, how much do 9 kites cost? (a) ₹45 (b) ₹190 (c) ₹342 (d) ₹171
34. 34.₹230 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹138 (b) ₹115 (c) ₹46 (d) ₹92
35. 35.₹370 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹185 (b) ₹370 (c) ₹37 (d) ₹333
36. 36.₹196 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹84 (b) ₹98 (c) ₹28 (d) ₹112
37. 37.₹384 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹32 (b) ₹192 (c) ₹224 (d) ₹160
38. 38.If 7 mangoes cost ₹168, how much do 10 mangoes cost? (a) ₹171 (b) ₹240 (c) ₹264 (d) ₹1680
39. 39.₹171 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹114 (b) ₹95 (c) ₹76 (d) ₹19
40. 40.₹81 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹72 (b) ₹73 (c) ₹81 (d) ₹9

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