Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 543 · 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 5 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 2 days (d) 8 days
2. 2.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 1 day
3. 3.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 15 days (d) 13 days
4. 4.₹99 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹81 (b) ₹27 (c) ₹72 (d) ₹9
5. 5.If 3 pens cost ₹48, how much do 12 pens cost? (a) ₹576 (b) ₹57 (c) ₹208 (d) ₹192
6. 6.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 33 days (b) 14 days (c) 32 days (d) 2 days
7. 7.₹70 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹35 (b) ₹14 (c) ₹70 (d) ₹56
8. 8.If 4 notebooks cost ₹72, how much do 11 notebooks cost? (a) ₹79 (b) ₹216 (c) ₹198 (d) ₹792
9. 9.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 39 days (d) 40 days
10. 10.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 49 days (c) 9 days (d) 19 days
11. 11.₹91 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹26 (b) ₹78 (c) ₹65 (d) ₹13
12. 12.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 15 days (d) 8 days
13. 13.₹84 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹84 (b) ₹42 (c) ₹14 (d) ₹70
14. 14.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 7 days
15. 15.₹450 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹45 (b) ₹450 (c) ₹225 (d) ₹405
16. 16.₹276 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹23 (b) ₹115 (c) ₹161 (d) ₹138
17. 17.₹40 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹20 (b) ₹30 (c) ₹40 (d) ₹10
18. 18.If 6 notebooks cost ₹42, how much do 11 notebooks cost? (a) ₹47 (b) ₹462 (c) ₹77 (d) ₹84
19. 19.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 13 days (c) 12 days (d) 11 days
20. 20.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 48 days (b) 3 days (c) 18 days (d) 6 days
21. 21.₹100 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹50 (b) ₹40 (c) ₹20 (d) ₹60
22. 22.If 9 notebooks cost ₹90, how much do 3 notebooks cost? (a) ₹30 (b) ₹84 (c) ₹40 (d) ₹270
23. 23.If 9 pens cost ₹162, how much do 7 pens cost? (a) ₹1134 (b) ₹144 (c) ₹126 (d) ₹160
24. 24.If 7 notebooks cost ₹147, how much do 5 notebooks cost? (a) ₹145 (b) ₹126 (c) ₹735 (d) ₹105
25. 25.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 9 days (d) 14 days
26. 26.If 6 kites cost ₹60, how much do 11 kites cost? (a) ₹660 (b) ₹120 (c) ₹110 (d) ₹65
27. 27.₹90 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹10 (b) ₹45 (c) ₹50 (d) ₹40
28. 28.₹210 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹30 (b) ₹105 (c) ₹120 (d) ₹90
29. 29.If 6 pens cost ₹96, how much do 11 pens cost? (a) ₹101 (b) ₹1056 (c) ₹192 (d) ₹176
30. 30.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 21 days (d) 1 day
31. 31.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 27 days (c) 17 days (d) 26 days
32. 32.If 2 kites cost ₹40, how much do 9 kites cost? (a) ₹47 (b) ₹200 (c) ₹180 (d) ₹360
33. 33.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 12 days (c) 16 days (d) 4 days
34. 34.If 5 mangoes cost ₹85, how much do 8 mangoes cost? (a) ₹88 (b) ₹153 (c) ₹680 (d) ₹136
35. 35.₹572 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹352 (b) ₹220 (c) ₹286 (d) ₹44
36. 36.If 2 kites cost ₹38, how much do 3 kites cost? (a) ₹57 (b) ₹39 (c) ₹76 (d) ₹114
37. 37.8 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 41 days (c) 10 days (d) 40 days
38. 38.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 12 days (c) 2 days (d) 19 days
39. 39.₹280 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹140 (b) ₹35 (c) ₹280 (d) ₹245
40. 40.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 20 days (c) 21 days (d) 11 days

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