Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 516 · 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.If 5 kites cost ₹45, how much do 2 kites cost? (a) ₹90 (b) ₹42 (c) ₹18 (d) ₹27
2. 2.₹234 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹18 (b) ₹144 (c) ₹117 (d) ₹90
3. 3.₹328 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹328 (b) ₹164 (c) ₹287 (d) ₹41
4. 4.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 13 days (d) 18 days
5. 5.If 2 notebooks cost ₹50, how much do 9 notebooks cost? (a) ₹450 (b) ₹250 (c) ₹225 (d) ₹57
6. 6.₹234 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹162 (b) ₹117 (c) ₹18 (d) ₹72
7. 7.₹410 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹41 (b) ₹205 (c) ₹287 (d) ₹123
8. 8.₹196 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹28 (b) ₹112 (c) ₹98 (d) ₹84
9. 9.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 18 days (d) 3 days
10. 10.6 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 14 days (b) 16 days (c) 10 days (d) 9 days
11. 11.₹180 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹180 (b) ₹18 (c) ₹162 (d) ₹90
12. 12.₹63 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹7 (b) ₹42 (c) ₹28 (d) ₹35
13. 13.If 2 kites cost ₹50, how much do 12 kites cost? (a) ₹600 (b) ₹325 (c) ₹300 (d) ₹60
14. 14.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 15 days (d) 14 days
15. 15.₹165 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹60 (b) ₹15 (c) ₹120 (d) ₹105
16. 16.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 64 days (b) 63 days (c) 7 days (d) 21 days
17. 17.₹90 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹45 (b) ₹20 (c) ₹10 (d) ₹70
18. 18.If 5 mangoes cost ₹15, how much do 2 mangoes cost? (a) ₹12 (b) ₹30 (c) ₹6 (d) ₹9
19. 19.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 10 days (c) 1 day (d) 17 days
20. 20.₹77 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹11 (b) ₹67 (c) ₹66 (d) ₹77
21. 21.If 5 kites cost ₹50, how much do 2 kites cost? (a) ₹100 (b) ₹47 (c) ₹30 (d) ₹20
22. 22.₹121 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹11 (b) ₹99 (c) ₹110 (d) ₹22
23. 23.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 21 days (c) 22 days (d) 1 day
24. 24.9 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 18 days (d) 8 days
25. 25.₹216 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹108 (b) ₹27 (c) ₹216 (d) ₹189
26. 26.If 7 kites cost ₹28, how much do 3 kites cost? (a) ₹12 (b) ₹16 (c) ₹24 (d) ₹84
27. 27.If 3 notebooks cost ₹45, how much do 8 notebooks cost? (a) ₹135 (b) ₹50 (c) ₹360 (d) ₹120
28. 28.If 9 notebooks cost ₹81, how much do 6 notebooks cost? (a) ₹78 (b) ₹54 (c) ₹63 (d) ₹486
29. 29.₹288 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹288 (b) ₹36 (c) ₹252 (d) ₹144
30. 30.If 4 pens cost ₹24, how much do 7 pens cost? (a) ₹48 (b) ₹168 (c) ₹42 (d) ₹27
31. 31.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 11 days (d) 8 days
32. 32.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 7 days (d) 28 days
33. 33.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 13 days (c) 4 days (d) 16 days
34. 34.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 5 days (d) 2 days
35. 35.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 9 days (d) 7 days
36. 36.₹560 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹200 (b) ₹360 (c) ₹40 (d) ₹280
37. 37.If 9 pens cost ₹81, how much do 6 pens cost? (a) ₹54 (b) ₹63 (c) ₹78 (d) ₹486
38. 38.If 2 pens cost ₹38, how much do 7 pens cost? (a) ₹266 (b) ₹152 (c) ₹43 (d) ₹133
39. 39.₹120 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹60 (b) ₹84 (c) ₹12 (d) ₹36
40. 40.If 8 kites cost ₹72, how much do 9 kites cost? (a) ₹81 (b) ₹90 (c) ₹648 (d) ₹73

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