Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 750 · 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. 1.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 1 day (c) 17 days (d) 10 days
2. 2.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 16 days (d) 10 days
3. 3.₹442 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹221 (b) ₹272 (c) ₹170 (d) ₹34
4. 4.If 9 mangoes cost ₹108, how much do 8 mangoes cost? (a) ₹108 (b) ₹96 (c) ₹864 (d) ₹107
5. 5.If 8 kites cost ₹176, how much do 3 kites cost? (a) ₹171 (b) ₹88 (c) ₹66 (d) ₹528
6. 6.₹468 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹324 (b) ₹144 (c) ₹36 (d) ₹234
7. 7.₹308 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹110 (b) ₹154 (c) ₹22 (d) ₹198
8. 8.₹56 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹28 (b) ₹42 (c) ₹56 (d) ₹14
9. 9.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 12 days (c) 3 days (d) 4 days
10. 10.₹390 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹351 (b) ₹39 (c) ₹195 (d) ₹390
11. 11.If 3 mangoes cost ₹21, how much do 10 mangoes cost? (a) ₹210 (b) ₹28 (c) ₹70 (d) ₹77
12. 12.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 29 days (c) 28 days (d) 13 days
13. 13.If 2 kites cost ₹6, how much do 3 kites cost? (a) ₹12 (b) ₹7 (c) ₹9 (d) ₹18
14. 14.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 3 days (d) 2 days
15. 15.3 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
16. 16.If 4 kites cost ₹68, how much do 6 kites cost? (a) ₹102 (b) ₹408 (c) ₹70 (d) ₹119
17. 17.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 10 days (d) 4 days
18. 18.₹261 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹116 (b) ₹29 (c) ₹174 (d) ₹145
19. 19.₹410 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹123 (b) ₹205 (c) ₹287 (d) ₹41
20. 20.If 7 notebooks cost ₹119, how much do 8 notebooks cost? (a) ₹136 (b) ₹952 (c) ₹153 (d) ₹120
21. 21.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 11 days (d) 8 days
22. 22.8 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 18 days (c) 9 days (d) 8 days
23. 23.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 5 days (d) 12 days
24. 24.3 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
25. 25.If 7 pens cost ₹28, how much do 8 pens cost? (a) ₹32 (b) ₹224 (c) ₹36 (d) ₹29
26. 26.If 2 kites cost ₹28, how much do 11 kites cost? (a) ₹308 (b) ₹168 (c) ₹154 (d) ₹37
27. 27.If 4 pens cost ₹48, how much do 5 pens cost? (a) ₹49 (b) ₹60 (c) ₹240 (d) ₹72
28. 28.₹420 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹150 (b) ₹30 (c) ₹210 (d) ₹270
29. 29.₹611 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹423 (b) ₹235 (c) ₹376 (d) ₹47
30. 30.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 28 days (b) 7 days (c) 10 days (d) 18 days
31. 31.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 17 days
32. 32.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 6 days (c) 4 days (d) 36 days
33. 33.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 6 days (c) 16 days (d) 4 days
34. 34.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 17 days (c) 1 day (d) 11 days
35. 35.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 18 days (d) 12 days
36. 36.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 63 days (b) 7 days (c) 64 days (d) 21 days
37. 37.₹506 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹92 (b) ₹46 (c) ₹414 (d) ₹253
38. 38.If 7 pens cost ₹21, how much do 9 pens cost? (a) ₹23 (b) ₹30 (c) ₹27 (d) ₹189
39. 39.₹135 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹15 (b) ₹120 (c) ₹135 (d) ₹121
40. 40.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 10 days (d) 1 day

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