Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 968 · 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. 1.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 7 days (c) 5 days (d) 6 days
2. 2.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 19 days (d) 3 days
3. 3.If 2 mangoes cost ₹10, how much do 4 mangoes cost? (a) ₹20 (b) ₹25 (c) ₹12 (d) ₹40
4. 4.₹182 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹26 (b) ₹91 (c) ₹182 (d) ₹156
5. 5.9 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) 5 days (d) 9 days
6. 6.₹234 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹234 (b) ₹208 (c) ₹26 (d) ₹117
7. 7.₹429 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹33 (b) ₹297 (c) ₹165 (d) ₹264
8. 8.₹153 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹136 (b) ₹34 (c) ₹119 (d) ₹17
9. 9.₹559 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹430 (b) ₹43 (c) ₹172 (d) ₹387
10. 10.₹171 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹19 (b) ₹114 (c) ₹95 (d) ₹76
11. 11.If 3 pens cost ₹18, how much do 4 pens cost? (a) ₹30 (b) ₹24 (c) ₹19 (d) ₹72
12. 12.₹259 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹259 (b) ₹223 (c) ₹222 (d) ₹37
13. 13.If 5 kites cost ₹35, how much do 12 kites cost? (a) ₹42 (b) ₹91 (c) ₹84 (d) ₹420
14. 14.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 17 days (d) 4 days
15. 15.₹121 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹44 (b) ₹88 (c) ₹11 (d) ₹77
16. 16.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 10 days (d) 3 days
17. 17.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 1 day (c) 3 days (d) 12 days
18. 18.₹90 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹10 (b) ₹45 (c) ₹40 (d) ₹50
19. 19.₹245 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹211 (b) ₹245 (c) ₹210 (d) ₹35
20. 20.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 29 days (c) 13 days (d) 28 days
21. 21.If 4 kites cost ₹48, how much do 12 kites cost? (a) ₹156 (b) ₹576 (c) ₹56 (d) ₹144
22. 22.If 3 notebooks cost ₹12, how much do 6 notebooks cost? (a) ₹72 (b) ₹24 (c) ₹15 (d) ₹28
23. 23.₹308 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹224 (b) ₹84 (c) ₹28 (d) ₹154
24. 24.₹123 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹83 (b) ₹82 (c) ₹123 (d) ₹41
25. 25.If 9 mangoes cost ₹108, how much do 8 mangoes cost? (a) ₹96 (b) ₹108 (c) ₹107 (d) ₹864
26. 26.If 3 pens cost ₹69, how much do 4 pens cost? (a) ₹70 (b) ₹276 (c) ₹115 (d) ₹92
27. 27.₹144 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹84 (b) ₹12 (c) ₹60 (d) ₹72
28. 28.If 4 pens cost ₹96, how much do 9 pens cost? (a) ₹240 (b) ₹101 (c) ₹216 (d) ₹864
29. 29.₹336 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹192 (b) ₹168 (c) ₹144 (d) ₹48
30. 30.If 3 kites cost ₹72, how much do 4 kites cost? (a) ₹288 (b) ₹120 (c) ₹73 (d) ₹96
31. 31.If 2 pens cost ₹14, how much do 10 pens cost? (a) ₹140 (b) ₹70 (c) ₹22 (d) ₹77
32. 32.₹35 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹35 (b) ₹29 (c) ₹7 (d) ₹28
33. 33.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 4 days (d) 6 days
34. 34.₹105 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹105 (b) ₹85 (c) ₹21 (d) ₹84
35. 35.₹539 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹392 (b) ₹49 (c) ₹196 (d) ₹343
36. 36.₹517 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹376 (b) ₹423 (c) ₹47 (d) ₹141
37. 37.₹264 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹192 (b) ₹132 (c) ₹24 (d) ₹72
38. 38.If 3 mangoes cost ₹9, how much do 12 mangoes cost? (a) ₹108 (b) ₹39 (c) ₹18 (d) ₹36
39. 39.₹72 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹24 (b) ₹36 (c) ₹72 (d) ₹48
40. 40.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 6 days (c) 9 days (d) 24 days

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