Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 779 · 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. 1.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 9 days (d) 10 days
2. 2.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 2 days (d) 3 days
3. 3.If 6 kites cost ₹48, how much do 5 kites cost? (a) ₹40 (b) ₹240 (c) ₹48 (d) ₹47
4. 4.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 17 days (b) 11 days (c) 7 days (d) 28 days
5. 5.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 1 day (b) 3 days (c) 2 days (d) 8 days
6. 6.₹245 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹210 (b) ₹35 (c) ₹175 (d) ₹70
7. 7.If 7 notebooks cost ₹175, how much do 5 notebooks cost? (a) ₹150 (b) ₹875 (c) ₹125 (d) ₹173
8. 8.If 3 kites cost ₹33, how much do 7 kites cost? (a) ₹88 (b) ₹231 (c) ₹37 (d) ₹77
9. 9.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 14 days (c) 6 days (d) 24 days
10. 10.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 26 days (b) 27 days (c) 16 days (d) 10 days
11. 11.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 15 days (c) 36 days (d) 37 days
12. 12.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 20 days (d) 6 days
13. 13.9 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 10 days (d) 8 days
14. 14.If 3 pens cost ₹15, how much do 4 pens cost? (a) ₹60 (b) ₹16 (c) ₹25 (d) ₹20
15. 15.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 14 days (c) 4 days (d) 15 days
16. 16.If 7 pens cost ₹91, how much do 6 pens cost? (a) ₹90 (b) ₹546 (c) ₹91 (d) ₹78
17. 17.₹400 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹50 (b) ₹400 (c) ₹350 (d) ₹200
18. 18.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 12 days (c) 11 days (d) 10 days
19. 19.If 3 mangoes cost ₹45, how much do 8 mangoes cost? (a) ₹50 (b) ₹135 (c) ₹120 (d) ₹360
20. 20.₹90 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹36 (b) ₹54 (c) ₹18 (d) ₹45
21. 21.₹91 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹28 (b) ₹63 (c) ₹7 (d) ₹70
22. 22.₹484 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹242 (b) ₹44 (c) ₹220 (d) ₹264
23. 23.8 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 24 days (b) 14 days (c) 25 days (d) 4 days
24. 24.If 4 pens cost ₹92, how much do 3 pens cost? (a) ₹92 (b) ₹91 (c) ₹276 (d) ₹69
25. 25.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 5 days (d) 4 days
26. 26.₹324 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹180 (b) ₹144 (c) ₹36 (d) ₹162
27. 27.If 2 kites cost ₹42, how much do 4 kites cost? (a) ₹44 (b) ₹168 (c) ₹84 (d) ₹105
28. 28.₹121 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹11 (b) ₹33 (c) ₹99 (d) ₹88
29. 29.₹207 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹92 (b) ₹115 (c) ₹23 (d) ₹138
30. 30.If 7 notebooks cost ₹147, how much do 10 notebooks cost? (a) ₹210 (b) ₹1470 (c) ₹150 (d) ₹231
31. 31.₹115 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹23 (b) ₹46 (c) ₹92 (d) ₹69
32. 32.If 2 mangoes cost ₹24, how much do 5 mangoes cost? (a) ₹27 (b) ₹60 (c) ₹72 (d) ₹120
33. 33.₹119 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹85 (b) ₹51 (c) ₹17 (d) ₹68
34. 34.₹132 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹84 (b) ₹48 (c) ₹12 (d) ₹66
35. 35.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 13 days (d) 4 days
36. 36.₹55 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹25 (b) ₹35 (c) ₹5 (d) ₹30
37. 37.If 8 notebooks cost ₹56, how much do 2 notebooks cost? (a) ₹112 (b) ₹14 (c) ₹50 (d) ₹21
38. 38.If 2 kites cost ₹42, how much do 7 kites cost? (a) ₹47 (b) ₹168 (c) ₹294 (d) ₹147
39. 39.₹270 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹81 (b) ₹27 (c) ₹135 (d) ₹189
40. 40.₹473 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹43 (b) ₹387 (c) ₹86 (d) ₹430

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