Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 830 · 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.₹91 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹7 (b) ₹70 (c) ₹63 (d) ₹28
2. 2.If 2 notebooks cost ₹20, how much do 9 notebooks cost? (a) ₹100 (b) ₹27 (c) ₹90 (d) ₹180
3. 3.₹300 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹50 (b) ₹300 (c) ₹250 (d) ₹150
4. 4.If 7 pens cost ₹91, how much do 8 pens cost? (a) ₹92 (b) ₹104 (c) ₹728 (d) ₹117
5. 5.₹55 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹11 (b) ₹33 (c) ₹44 (d) ₹22
6. 6.If 8 pens cost ₹64, how much do 9 pens cost? (a) ₹72 (b) ₹576 (c) ₹65 (d) ₹80
7. 7.₹492 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹205 (b) ₹41 (c) ₹246 (d) ₹287
8. 8.If 5 kites cost ₹125, how much do 11 kites cost? (a) ₹1375 (b) ₹300 (c) ₹131 (d) ₹275
9. 9.₹65 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹52 (b) ₹39 (c) ₹26 (d) ₹13
10. 10.If 2 notebooks cost ₹24, how much do 11 notebooks cost? (a) ₹132 (b) ₹33 (c) ₹144 (d) ₹264
11. 11.If 6 kites cost ₹78, how much do 7 kites cost? (a) ₹79 (b) ₹104 (c) ₹91 (d) ₹546
12. 12.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 15 days (c) 27 days (d) 3 days
13. 13.If 4 kites cost ₹36, how much do 2 kites cost? (a) ₹18 (b) ₹72 (c) ₹27 (d) ₹34
14. 14.If 5 pens cost ₹100, how much do 6 pens cost? (a) ₹600 (b) ₹120 (c) ₹101 (d) ₹140
15. 15.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 3 days (c) 48 days (d) 6 days
16. 16.If 8 mangoes cost ₹176, how much do 9 mangoes cost? (a) ₹198 (b) ₹177 (c) ₹220 (d) ₹1584
17. 17.If 6 kites cost ₹30, how much do 5 kites cost? (a) ₹30 (b) ₹29 (c) ₹25 (d) ₹150
18. 18.₹72 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹36 (b) ₹72 (c) ₹64 (d) ₹8
19. 19.₹616 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹396 (b) ₹44 (c) ₹308 (d) ₹220
20. 20.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 29 days (c) 3 days (d) 13 days
21. 21.If 8 mangoes cost ₹96, how much do 4 mangoes cost? (a) ₹48 (b) ₹60 (c) ₹92 (d) ₹384
22. 22.If 8 mangoes cost ₹152, how much do 12 mangoes cost? (a) ₹247 (b) ₹228 (c) ₹1824 (d) ₹156
23. 23.₹81 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹27 (b) ₹81 (c) ₹55 (d) ₹54
24. 24.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 12 days (d) 4 days
25. 25.₹196 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹126 (b) ₹70 (c) ₹14 (d) ₹98
26. 26.If 2 notebooks cost ₹30, how much do 9 notebooks cost? (a) ₹37 (b) ₹270 (c) ₹135 (d) ₹150
27. 27.If 3 kites cost ₹51, how much do 2 kites cost? (a) ₹102 (b) ₹51 (c) ₹34 (d) ₹50
28. 28.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 32 days (d) 33 days
29. 29.₹48 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹24 (b) ₹48 (c) ₹6 (d) ₹42
30. 30.If 8 kites cost ₹136, how much do 9 kites cost? (a) ₹1224 (b) ₹170 (c) ₹137 (d) ₹153
31. 31.₹342 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹152 (b) ₹171 (c) ₹38 (d) ₹190
32. 32.₹275 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹25 (b) ₹75 (c) ₹225 (d) ₹200
33. 33.If 7 kites cost ₹63, how much do 4 kites cost? (a) ₹252 (b) ₹60 (c) ₹45 (d) ₹36
34. 34.₹423 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹376 (b) ₹377 (c) ₹423 (d) ₹47
35. 35.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹44 (b) ₹48 (c) ₹40 (d) ₹8
36. 36.If 8 kites cost ₹56, how much do 5 kites cost? (a) ₹42 (b) ₹35 (c) ₹53 (d) ₹280
37. 37.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 18 days (d) 3 days
38. 38.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 29 days (b) 8 days (c) 28 days (d) 16 days
39. 39.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 40 days (d) 39 days
40. 40.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 45 days (b) 5 days (c) 7 days (d) 23 days

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