Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 889 · 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. 1.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 18 days (c) 10 days (d) 19 days
2. 2.If 5 notebooks cost ₹90, how much do 2 notebooks cost? (a) ₹54 (b) ₹180 (c) ₹87 (d) ₹36
3. 3.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 55 days (b) 54 days (c) 5 days (d) 19 days
4. 4.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 28 days (d) 18 days
5. 5.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 7 days (d) 4 days
6. 6.If 5 kites cost ₹125, how much do 9 kites cost? (a) ₹250 (b) ₹225 (c) ₹1125 (d) ₹129
7. 7.If 9 mangoes cost ₹144, how much do 2 mangoes cost? (a) ₹137 (b) ₹32 (c) ₹288 (d) ₹48
8. 8.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 19 days (b) 12 days (c) 18 days (d) 16 days
9. 9.If 7 notebooks cost ₹105, how much do 10 notebooks cost? (a) ₹165 (b) ₹108 (c) ₹150 (d) ₹1050
10. 10.₹328 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹41 (b) ₹287 (c) ₹164 (d) ₹328
11. 11.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 28 days (c) 15 days (d) 3 days
12. 12.₹564 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹47 (b) ₹235 (c) ₹282 (d) ₹329
13. 13.If 9 pens cost ₹162, how much do 10 pens cost? (a) ₹163 (b) ₹180 (c) ₹198 (d) ₹1620
14. 14.If 9 pens cost ₹45, how much do 12 pens cost? (a) ₹540 (b) ₹65 (c) ₹60 (d) ₹48
15. 15.If 8 kites cost ₹144, how much do 10 kites cost? (a) ₹198 (b) ₹180 (c) ₹1440 (d) ₹146
16. 16.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 16 days (c) 6 days (d) 5 days
17. 17.₹209 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹95 (b) ₹114 (c) ₹133 (d) ₹19
18. 18.If 4 notebooks cost ₹32, how much do 9 notebooks cost? (a) ₹288 (b) ₹37 (c) ₹80 (d) ₹72
19. 19.If 5 notebooks cost ₹25, how much do 3 notebooks cost? (a) ₹20 (b) ₹23 (c) ₹15 (d) ₹75
20. 20.If 7 mangoes cost ₹154, how much do 8 mangoes cost? (a) ₹155 (b) ₹1232 (c) ₹176 (d) ₹198
21. 21.6 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 13 days (b) 6 days (c) 10 days (d) 12 days
22. 22.₹99 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹22 (b) ₹11 (c) ₹88 (d) ₹77
23. 23.₹380 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹114 (b) ₹266 (c) ₹38 (d) ₹190
24. 24.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 6 days (d) 10 days
25. 25.₹70 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹70 (b) ₹10 (c) ₹35 (d) ₹60
26. 26.6 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) 16 days (d) 4 days
27. 27.If 2 notebooks cost ₹12, how much do 6 notebooks cost? (a) ₹16 (b) ₹36 (c) ₹42 (d) ₹72
28. 28.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 19 days (c) 18 days (d) 6 days
29. 29.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 8 days (d) 1 day
30. 30.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 17 days (d) 16 days
31. 31.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 8 days (d) 2 days
32. 32.₹572 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹44 (b) ₹352 (c) ₹220 (d) ₹286
33. 33.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 1 day (c) 22 days (d) 21 days
34. 34.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 40 days (c) 39 days (d) 19 days
35. 35.If 2 pens cost ₹20, how much do 3 pens cost? (a) ₹60 (b) ₹30 (c) ₹21 (d) ₹40
36. 36.If 5 pens cost ₹85, how much do 9 pens cost? (a) ₹153 (b) ₹170 (c) ₹89 (d) ₹765
37. 37.₹468 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹144 (b) ₹234 (c) ₹324 (d) ₹36
38. 38.6 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 19 days (b) 25 days (c) 11 days (d) 9 days
39. 39.₹147 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹105 (b) ₹84 (c) ₹21 (d) ₹63
40. 40.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 31 days (c) 18 days (d) 30 days

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