Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 647 · 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. 1.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 9 days (d) 7 days
2. 2.If 8 mangoes cost ₹40, how much do 5 mangoes cost? (a) ₹200 (b) ₹30 (c) ₹37 (d) ₹25
3. 3.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 3 days (c) 9 days (d) 15 days
4. 4.If 6 mangoes cost ₹36, how much do 5 mangoes cost? (a) ₹180 (b) ₹36 (c) ₹35 (d) ₹30
5. 5.₹248 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹248 (b) ₹31 (c) ₹124 (d) ₹217
6. 6.₹253 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹69 (b) ₹23 (c) ₹207 (d) ₹184
7. 7.5 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 31 days (b) 30 days (c) 9 days (d) 15 days
8. 8.₹481 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹37 (b) ₹148 (c) ₹370 (d) ₹333
9. 9.If 2 mangoes cost ₹38, how much do 3 mangoes cost? (a) ₹114 (b) ₹76 (c) ₹57 (d) ₹39
10. 10.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 22 days (c) 13 days (d) 21 days
11. 11.If 8 kites cost ₹184, how much do 5 kites cost? (a) ₹920 (b) ₹181 (c) ₹138 (d) ₹115
12. 12.₹406 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹203 (b) ₹29 (c) ₹261 (d) ₹145
13. 13.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 7 days (c) 19 days (d) 11 days
14. 14.₹455 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹175 (b) ₹35 (c) ₹280 (d) ₹315
15. 15.If 3 mangoes cost ₹72, how much do 12 mangoes cost? (a) ₹864 (b) ₹81 (c) ₹312 (d) ₹288
16. 16.₹143 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹65 (b) ₹91 (c) ₹13 (d) ₹78
17. 17.If 3 pens cost ₹57, how much do 7 pens cost? (a) ₹61 (b) ₹152 (c) ₹133 (d) ₹399
18. 18.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 13 days (c) 16 days (d) 17 days
19. 19.If 8 notebooks cost ₹40, how much do 2 notebooks cost? (a) ₹80 (b) ₹10 (c) ₹15 (d) ₹34
20. 20.₹120 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹48 (b) ₹24 (c) ₹60 (d) ₹72
21. 21.If 8 notebooks cost ₹64, how much do 11 notebooks cost? (a) ₹67 (b) ₹88 (c) ₹704 (d) ₹96
22. 22.If 3 notebooks cost ₹45, how much do 5 notebooks cost? (a) ₹75 (b) ₹225 (c) ₹90 (d) ₹47
23. 23.6 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 8 days (c) 16 days (d) 12 days
24. 24.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 11 days (c) 13 days (d) 16 days
25. 25.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 4 days (d) 3 days
26. 26.₹234 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹18 (b) ₹117 (c) ₹162 (d) ₹72
27. 27.₹95 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹19 (b) ₹57 (c) ₹38 (d) ₹76
28. 28.If 7 kites cost ₹133, how much do 4 kites cost? (a) ₹95 (b) ₹532 (c) ₹76 (d) ₹130
29. 29.₹448 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹32 (b) ₹224 (c) ₹160 (d) ₹288
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) 1 day (d) 21 days
31. 31.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 2 days (d) 19 days
32. 32.If 5 kites cost ₹105, how much do 2 kites cost? (a) ₹63 (b) ₹102 (c) ₹210 (d) ₹42
33. 33.₹135 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹54 (b) ₹27 (c) ₹108 (d) ₹81
34. 34.₹36 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹12 (b) ₹36 (c) ₹18 (d) ₹24
35. 35.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 7 days (d) 6 days
36. 36.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 5 days (d) 8 days
37. 37.₹84 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹14 (b) ₹84 (c) ₹42 (d) ₹70
38. 38.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 9 days
39. 39.₹462 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹252 (b) ₹231 (c) ₹210 (d) ₹42
40. 40.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹44 (b) ₹11 (c) ₹55 (d) ₹66

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