Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 598 · 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 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 10 days (d) 8 days
2. 2.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 30 days (b) 31 days (c) 18 days (d) 12 days
3. 3.If 5 kites cost ₹70, how much do 6 kites cost? (a) ₹98 (b) ₹71 (c) ₹420 (d) ₹84
4. 4.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 8 days (d) 7 days
5. 5.₹25 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹5 (b) ₹15 (c) ₹20 (d) ₹10
6. 6.₹336 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹96 (b) ₹240 (c) ₹48 (d) ₹168
7. 7.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 15 days (d) 14 days
8. 8.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 17 days (d) 9 days
9. 9.₹164 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹41 (b) ₹82 (c) ₹123 (d) ₹164
10. 10.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹9 (b) ₹81 (c) ₹45 (d) ₹72
11. 11.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 41 days (c) 40 days (d) 4 days
12. 12.₹279 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹31 (b) ₹186 (c) ₹124 (d) ₹155
13. 13.If 8 mangoes cost ₹72, how much do 7 mangoes cost? (a) ₹71 (b) ₹504 (c) ₹63 (d) ₹72
14. 14.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 53 days (b) 7 days (c) 19 days (d) 52 days
15. 15.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 19 days (c) 4 days (d) 2 days
16. 16.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 11 days (d) 4 days
17. 17.₹189 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹27 (b) ₹162 (c) ₹189 (d) ₹163
18. 18.9 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) 3 days (d) 15 days
19. 19.₹360 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹180 (b) ₹108 (c) ₹252 (d) ₹36
20. 20.₹481 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹37 (b) ₹185 (c) ₹296 (d) ₹333
21. 21.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 17 days (c) 33 days (d) 34 days
22. 22.If 4 kites cost ₹24, how much do 5 kites cost? (a) ₹36 (b) ₹30 (c) ₹25 (d) ₹120
23. 23.If 7 mangoes cost ₹21, how much do 5 mangoes cost? (a) ₹18 (b) ₹15 (c) ₹19 (d) ₹105
24. 24.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 11 days (d) 3 days
25. 25.6 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 14 days (d) 7 days
26. 26.₹440 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹396 (b) ₹440 (c) ₹44 (d) ₹220
27. 27.₹150 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹45 (b) ₹15 (c) ₹105 (d) ₹75
28. 28.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 60 days (b) 9 days (c) 61 days (d) 21 days
29. 29.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 42 days (b) 8 days (c) 20 days (d) 43 days
30. 30.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 13 days (d) 12 days
31. 31.If 8 pens cost ₹48, how much do 9 pens cost? (a) ₹60 (b) ₹54 (c) ₹49 (d) ₹432
32. 32.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 17 days (c) 6 days (d) 4 days
33. 33.If 9 mangoes cost ₹81, how much do 6 mangoes cost? (a) ₹486 (b) ₹63 (c) ₹54 (d) ₹78
34. 34.If 2 kites cost ₹14, how much do 4 kites cost? (a) ₹28 (b) ₹16 (c) ₹56 (d) ₹35
35. 35.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 17 days (b) 28 days (c) 11 days (d) 7 days
36. 36.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 16 days (d) 7 days
37. 37.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 11 days (c) 4 days (d) 16 days
38. 38.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 25 days (d) 17 days
39. 39.₹135 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹15 (b) ₹30 (c) ₹120 (d) ₹105
40. 40.₹150 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹150 (b) ₹125 (c) ₹75 (d) ₹25

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