Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 451 · 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. 1.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 28 days (c) 27 days (d) 15 days
2. 2.₹396 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹108 (b) ₹36 (c) ₹288 (d) ₹198
3. 3.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 24 days (b) 15 days (c) 9 days (d) 6 days
4. 4.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 40 days (c) 17 days (d) 39 days
5. 5.₹45 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹45 (b) ₹31 (c) ₹30 (d) ₹15
6. 6.If 5 mangoes cost ₹40, how much do 12 mangoes cost? (a) ₹480 (b) ₹96 (c) ₹104 (d) ₹47
7. 7.If 5 mangoes cost ₹80, how much do 4 mangoes cost? (a) ₹320 (b) ₹64 (c) ₹79 (d) ₹80
8. 8.If 5 mangoes cost ₹60, how much do 6 mangoes cost? (a) ₹84 (b) ₹72 (c) ₹61 (d) ₹360
9. 9.If 6 pens cost ₹108, how much do 8 pens cost? (a) ₹162 (b) ₹864 (c) ₹110 (d) ₹144
10. 10.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 4 days (d) 3 days
11. 11.If 9 pens cost ₹117, how much do 7 pens cost? (a) ₹91 (b) ₹819 (c) ₹115 (d) ₹104
12. 12.₹63 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹7 (b) ₹28 (c) ₹35 (d) ₹42
13. 13.If 5 notebooks cost ₹110, how much do 9 notebooks cost? (a) ₹114 (b) ₹220 (c) ₹990 (d) ₹198
14. 14.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 17 days (d) 9 days
15. 15.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 9 days (c) 4 days (d) 19 days
16. 16.₹52 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹26 (b) ₹13 (c) ₹52 (d) ₹39
17. 17.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 4 days (d) 10 days
18. 18.₹54 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹12 (b) ₹27 (c) ₹6 (d) ₹42
19. 19.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 8 days (d) 1 day
20. 20.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 13 days (b) 1 day (c) 2 days (d) 16 days
21. 21.₹55 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹35 (b) ₹40 (c) ₹20 (d) ₹5
22. 22.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 13 days (d) 28 days
23. 23.₹418 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹38 (b) ₹342 (c) ₹76 (d) ₹209
24. 24.If 5 kites cost ₹105, how much do 11 kites cost? (a) ₹1155 (b) ₹231 (c) ₹111 (d) ₹252
25. 25.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 14 days (c) 13 days (d) 15 days
26. 26.₹91 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹70 (b) ₹7 (c) ₹28 (d) ₹63
27. 27.If 7 pens cost ₹35, how much do 6 pens cost? (a) ₹30 (b) ₹210 (c) ₹35 (d) ₹34
28. 28.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 5 days (c) 12 days (d) 8 days
29. 29.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 20 days (b) 6 days (c) 15 days (d) 5 days
30. 30.₹99 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹11 (b) ₹99 (c) ₹88 (d) ₹89
31. 31.If 4 mangoes cost ₹28, how much do 11 mangoes cost? (a) ₹84 (b) ₹77 (c) ₹308 (d) ₹35
32. 32.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 9 days (d) 2 days
33. 33.If 3 pens cost ₹33, how much do 4 pens cost? (a) ₹132 (b) ₹44 (c) ₹55 (d) ₹34
34. 34.₹108 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹45 (b) ₹9 (c) ₹54 (d) ₹63
35. 35.₹348 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹145 (b) ₹174 (c) ₹29 (d) ₹203
36. 36.₹64 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹32 (b) ₹40 (c) ₹24 (d) ₹8
37. 37.If 5 kites cost ₹45, how much do 3 kites cost? (a) ₹43 (b) ₹135 (c) ₹27 (d) ₹36
38. 38.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 21 days (c) 1 day (d) 22 days
39. 39.If 7 pens cost ₹63, how much do 8 pens cost? (a) ₹72 (b) ₹504 (c) ₹64 (d) ₹81
40. 40.If 9 notebooks cost ₹189, how much do 7 notebooks cost? (a) ₹187 (b) ₹147 (c) ₹168 (d) ₹1323

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