Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 738 · 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. 1.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 2 days (d) 11 days
2. 2.If 3 kites cost ₹36, how much do 4 kites cost? (a) ₹144 (b) ₹48 (c) ₹60 (d) ₹37
3. 3.If 6 pens cost ₹132, how much do 2 pens cost? (a) ₹128 (b) ₹66 (c) ₹44 (d) ₹264
4. 4.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 2 days (c) 6 days (d) 8 days
5. 5.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 5 days
6. 6.8 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 9 days (d) 19 days
7. 7.If 9 pens cost ₹108, how much do 11 pens cost? (a) ₹1188 (b) ₹144 (c) ₹132 (d) ₹110
8. 8.If 4 pens cost ₹72, how much do 6 pens cost? (a) ₹432 (b) ₹74 (c) ₹126 (d) ₹108
9. 9.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 6 days (d) 8 days
10. 10.If 8 mangoes cost ₹24, how much do 5 mangoes cost? (a) ₹18 (b) ₹120 (c) ₹15 (d) ₹21
11. 11.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 1 day (d) 17 days
12. 12.If 4 kites cost ₹36, how much do 2 kites cost? (a) ₹34 (b) ₹18 (c) ₹27 (d) ₹72
13. 13.₹350 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹150 (b) ₹200 (c) ₹50 (d) ₹175
14. 14.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 12 days (c) 14 days (d) 16 days
15. 15.If 2 notebooks cost ₹44, how much do 3 notebooks cost? (a) ₹45 (b) ₹132 (c) ₹66 (d) ₹88
16. 16.₹231 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹231 (b) ₹199 (c) ₹33 (d) ₹198
17. 17.₹396 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹198 (b) ₹220 (c) ₹44 (d) ₹176
18. 18.If 6 pens cost ₹42, how much do 9 pens cost? (a) ₹378 (b) ₹45 (c) ₹70 (d) ₹63
19. 19.If 4 kites cost ₹96, how much do 5 kites cost? (a) ₹97 (b) ₹480 (c) ₹144 (d) ₹120
20. 20.₹99 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹72 (b) ₹27 (c) ₹9 (d) ₹81
21. 21.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 7 days (c) 6 days (d) 8 days
22. 22.₹264 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹99 (b) ₹132 (c) ₹165 (d) ₹33
23. 23.₹110 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹10 (b) ₹40 (c) ₹55 (d) ₹70
24. 24.If 2 pens cost ₹36, how much do 4 pens cost? (a) ₹144 (b) ₹90 (c) ₹38 (d) ₹72
25. 25.If 7 notebooks cost ₹42, how much do 10 notebooks cost? (a) ₹66 (b) ₹60 (c) ₹420 (d) ₹45
26. 26.If 9 kites cost ₹144, how much do 10 kites cost? (a) ₹1440 (b) ₹160 (c) ₹176 (d) ₹145
27. 27.₹342 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹171 (b) ₹38 (c) ₹76 (d) ₹266
28. 28.₹144 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹72 (b) ₹144 (c) ₹128 (d) ₹16
29. 29.If 3 kites cost ₹12, how much do 9 kites cost? (a) ₹18 (b) ₹36 (c) ₹40 (d) ₹108
30. 30.If 6 kites cost ₹90, how much do 11 kites cost? (a) ₹990 (b) ₹165 (c) ₹95 (d) ₹180
31. 31.If 7 pens cost ₹126, how much do 2 pens cost? (a) ₹36 (b) ₹121 (c) ₹252 (d) ₹54
32. 32.₹658 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹47 (b) ₹423 (c) ₹235 (d) ₹329
33. 33.₹434 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹217 (b) ₹31 (c) ₹155 (d) ₹279
34. 34.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 53 days (b) 19 days (c) 52 days (d) 7 days
35. 35.₹75 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹50 (b) ₹25 (c) ₹51 (d) ₹75
36. 36.If 5 mangoes cost ₹95, how much do 8 mangoes cost? (a) ₹760 (b) ₹98 (c) ₹152 (d) ₹171
37. 37.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 24 days (c) 10 days (d) 6 days
38. 38.If 3 mangoes cost ₹15, how much do 6 mangoes cost? (a) ₹35 (b) ₹18 (c) ₹30 (d) ₹90
39. 39.If 2 kites cost ₹26, how much do 3 kites cost? (a) ₹52 (b) ₹39 (c) ₹27 (d) ₹78
40. 40.If 7 pens cost ₹105, how much do 6 pens cost? (a) ₹104 (b) ₹90 (c) ₹630 (d) ₹105

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