Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 970 · 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 3 notebooks cost ₹54, how much do 2 notebooks cost? (a) ₹108 (b) ₹53 (c) ₹36 (d) ₹54
2. 2.If 5 mangoes cost ₹75, how much do 7 mangoes cost? (a) ₹105 (b) ₹77 (c) ₹120 (d) ₹525
3. 3.₹451 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹205 (b) ₹287 (c) ₹41 (d) ₹246
4. 4.If 5 kites cost ₹115, how much do 2 kites cost? (a) ₹46 (b) ₹69 (c) ₹112 (d) ₹230
5. 5.₹470 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹329 (b) ₹235 (c) ₹141 (d) ₹47
6. 6.₹170 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹153 (b) ₹17 (c) ₹85 (d) ₹170
7. 7.If 6 pens cost ₹54, how much do 7 pens cost? (a) ₹63 (b) ₹378 (c) ₹72 (d) ₹55
8. 8.₹208 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹64 (b) ₹16 (c) ₹144 (d) ₹104
9. 9.If 9 kites cost ₹225, how much do 10 kites cost? (a) ₹2250 (b) ₹226 (c) ₹250 (d) ₹275
10. 10.₹473 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹258 (b) ₹301 (c) ₹43 (d) ₹215
11. 11.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 45 days (c) 5 days (d) 9 days
12. 12.₹114 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹114 (b) ₹76 (c) ₹57 (d) ₹38
13. 13.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 17 days (c) 11 days (d) 35 days
14. 14.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 26 days (c) 27 days (d) 15 days
15. 15.If 2 mangoes cost ₹12, how much do 3 mangoes cost? (a) ₹18 (b) ₹36 (c) ₹13 (d) ₹24
16. 16.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 11 days (b) 6 days (c) 5 days (d) 4 days
17. 17.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 39 days (c) 40 days (d) 19 days
18. 18.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 9 days (d) 8 days
19. 19.If 2 kites cost ₹38, how much do 5 kites cost? (a) ₹190 (b) ₹114 (c) ₹41 (d) ₹95
20. 20.If 4 mangoes cost ₹24, how much do 5 mangoes cost? (a) ₹30 (b) ₹25 (c) ₹36 (d) ₹120
21. 21.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 24 days (b) 2 days (c) 25 days (d) 14 days
22. 22.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 13 days (c) 4 days (d) 7 days
23. 23.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 4 days (c) 16 days (d) 41 days
24. 24.If 5 notebooks cost ₹15, how much do 3 notebooks cost? (a) ₹45 (b) ₹13 (c) ₹9 (d) ₹12
25. 25.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 15 days (d) 3 days
26. 26.If 3 mangoes cost ₹24, how much do 4 mangoes cost? (a) ₹96 (b) ₹32 (c) ₹40 (d) ₹25
27. 27.If 2 notebooks cost ₹50, how much do 6 notebooks cost? (a) ₹150 (b) ₹300 (c) ₹175 (d) ₹54
28. 28.If 4 kites cost ₹12, how much do 7 kites cost? (a) ₹21 (b) ₹84 (c) ₹24 (d) ₹15
29. 29.If 3 notebooks cost ₹12, how much do 12 notebooks cost? (a) ₹21 (b) ₹52 (c) ₹48 (d) ₹144
30. 30.₹25 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹25 (b) ₹21 (c) ₹20 (d) ₹5
31. 31.If 4 kites cost ₹36, how much do 9 kites cost? (a) ₹90 (b) ₹41 (c) ₹81 (d) ₹324
32. 32.If 8 mangoes cost ₹112, how much do 5 mangoes cost? (a) ₹560 (b) ₹109 (c) ₹84 (d) ₹70
33. 33.If 2 kites cost ₹24, how much do 12 kites cost? (a) ₹34 (b) ₹144 (c) ₹288 (d) ₹156
34. 34.If 8 pens cost ₹88, how much do 2 pens cost? (a) ₹176 (b) ₹22 (c) ₹33 (d) ₹82
35. 35.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 1 day (c) 2 days (d) 13 days
36. 36.If 2 kites cost ₹12, how much do 10 kites cost? (a) ₹60 (b) ₹20 (c) ₹120 (d) ₹66
37. 37.If 4 notebooks cost ₹12, how much do 5 notebooks cost? (a) ₹15 (b) ₹18 (c) ₹60 (d) ₹13
38. 38.If 2 kites cost ₹38, how much do 6 kites cost? (a) ₹42 (b) ₹228 (c) ₹133 (d) ₹114
39. 39.₹145 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹145 (b) ₹29 (c) ₹117 (d) ₹116
40. 40.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 3 days (d) 9 days

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