Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 556 · 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 8 notebooks cost ₹104, how much do 6 notebooks cost? (a) ₹78 (b) ₹91 (c) ₹624 (d) ₹102
2. 2.₹658 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹47 (b) ₹329 (c) ₹423 (d) ₹235
3. 3.If 8 pens cost ₹24, how much do 5 pens cost? (a) ₹120 (b) ₹21 (c) ₹18 (d) ₹15
4. 4.If 5 kites cost ₹90, how much do 2 kites cost? (a) ₹54 (b) ₹180 (c) ₹87 (d) ₹36
5. 5.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 8 days (d) 7 days
6. 6.₹49 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹49 (b) ₹7 (c) ₹42 (d) ₹43
7. 7.₹192 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹120 (b) ₹24 (c) ₹72 (d) ₹96
8. 8.₹240 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹210 (b) ₹120 (c) ₹240 (d) ₹30
9. 9.If 2 mangoes cost ₹18, how much do 12 mangoes cost? (a) ₹28 (b) ₹117 (c) ₹108 (d) ₹216
10. 10.If 4 kites cost ₹28, how much do 12 kites cost? (a) ₹91 (b) ₹336 (c) ₹36 (d) ₹84
11. 11.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 14 days (c) 22 days (d) 23 days
12. 12.₹287 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹123 (b) ₹41 (c) ₹205 (d) ₹164
13. 13.If 9 pens cost ₹81, how much do 2 pens cost? (a) ₹27 (b) ₹74 (c) ₹18 (d) ₹162
14. 14.If 8 pens cost ₹56, how much do 7 pens cost? (a) ₹56 (b) ₹55 (c) ₹49 (d) ₹392
15. 15.If 3 notebooks cost ₹51, how much do 7 notebooks cost? (a) ₹136 (b) ₹119 (c) ₹55 (d) ₹357
16. 16.If 8 pens cost ₹48, how much do 4 pens cost? (a) ₹30 (b) ₹24 (c) ₹44 (d) ₹192
17. 17.If 6 mangoes cost ₹72, how much do 2 mangoes cost? (a) ₹144 (b) ₹68 (c) ₹36 (d) ₹24
18. 18.₹189 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹126 (b) ₹21 (c) ₹84 (d) ₹105
19. 19.If 4 kites cost ₹12, how much do 5 kites cost? (a) ₹60 (b) ₹13 (c) ₹15 (d) ₹18
20. 20.₹451 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹410 (b) ₹41 (c) ₹82 (d) ₹369
21. 21.₹234 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹117 (b) ₹26 (c) ₹104 (d) ₹130
22. 22.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 45 days (b) 9 days (c) 21 days (d) 5 days
23. 23.If 7 mangoes cost ₹28, how much do 8 mangoes cost? (a) ₹36 (b) ₹224 (c) ₹32 (d) ₹29
24. 24.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 35 days (c) 15 days (d) 5 days
25. 25.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 7 days (d) 2 days
26. 26.If 8 notebooks cost ₹152, how much do 6 notebooks cost? (a) ₹912 (b) ₹133 (c) ₹114 (d) ₹150
27. 27.If 2 notebooks cost ₹6, how much do 8 notebooks cost? (a) ₹27 (b) ₹12 (c) ₹48 (d) ₹24
28. 28.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 20 days (c) 6 days (d) 14 days
29. 29.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 13 days (c) 25 days (d) 4 days
30. 30.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 4 days (d) 19 days
31. 31.₹21 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹7 (b) ₹15 (c) ₹14 (d) ₹21
32. 32.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 7 days (d) 4 days
33. 33.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 32 days (b) 2 days (c) 17 days (d) 3 days
34. 34.₹130 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹26 (b) ₹78 (c) ₹52 (d) ₹65
35. 35.₹40 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹40 (b) ₹20 (c) ₹32 (d) ₹8
36. 36.₹546 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹351 (b) ₹195 (c) ₹39 (d) ₹273
37. 37.₹108 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹12 (b) ₹24 (c) ₹84 (d) ₹54
38. 38.₹121 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹77 (b) ₹88 (c) ₹11 (d) ₹44
39. 39.If 5 notebooks cost ₹15, how much do 2 notebooks cost? (a) ₹9 (b) ₹30 (c) ₹12 (d) ₹6
40. 40.If 7 mangoes cost ₹154, how much do 12 mangoes cost? (a) ₹1848 (b) ₹159 (c) ₹286 (d) ₹264

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