Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 23 · 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. 1.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 22 days (c) 21 days (d) 11 days
2. 2.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 17 days (c) 3 days (d) 32 days
3. 3.₹351 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹108 (b) ₹270 (c) ₹243 (d) ₹27
4. 4.₹198 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹99 (b) ₹72 (c) ₹18 (d) ₹126
5. 5.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 4 days (d) 5 days
6. 6.₹369 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹164 (b) ₹246 (c) ₹205 (d) ₹41
7. 7.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 4 days (c) 27 days (d) 3 days
8. 8.₹21 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹21 (b) ₹14 (c) ₹15 (d) ₹7
9. 9.If 6 pens cost ₹126, how much do 7 pens cost? (a) ₹127 (b) ₹882 (c) ₹168 (d) ₹147
10. 10.If 4 pens cost ₹84, how much do 8 pens cost? (a) ₹672 (b) ₹88 (c) ₹168 (d) ₹189
11. 11.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 1 day (c) 8 days (d) 3 days
12. 12.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 13 days (d) 17 days
13. 13.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 1 day (c) 10 days (d) 7 days
14. 14.If 3 pens cost ₹18, how much do 10 pens cost? (a) ₹25 (b) ₹60 (c) ₹180 (d) ₹66
15. 15.If 9 pens cost ₹81, how much do 12 pens cost? (a) ₹108 (b) ₹972 (c) ₹117 (d) ₹84
16. 16.₹140 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹70 (b) ₹100 (c) ₹40 (d) ₹20
17. 17.If 9 pens cost ₹27, how much do 7 pens cost? (a) ₹189 (b) ₹21 (c) ₹24 (d) ₹25
18. 18.If 7 notebooks cost ₹175, how much do 11 notebooks cost? (a) ₹1925 (b) ₹275 (c) ₹179 (d) ₹300
19. 19.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 1 day (c) 6 days (d) 8 days
20. 20.₹110 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹110 (b) ₹22 (c) ₹88 (d) ₹55
21. 21.₹380 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹190 (b) ₹38 (c) ₹114 (d) ₹266
22. 22.₹378 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹42 (b) ₹378 (c) ₹189 (d) ₹336
23. 23.If 8 pens cost ₹112, how much do 9 pens cost? (a) ₹140 (b) ₹113 (c) ₹126 (d) ₹1008
24. 24.₹312 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹195 (b) ₹156 (c) ₹39 (d) ₹117
25. 25.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 21 days (d) 6 days
26. 26.If 6 kites cost ₹102, how much do 5 kites cost? (a) ₹101 (b) ₹102 (c) ₹510 (d) ₹85
27. 27.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 7 days (d) 11 days
28. 28.₹126 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹63 (b) ₹18 (c) ₹54 (d) ₹72
29. 29.₹123 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹83 (b) ₹41 (c) ₹123 (d) ₹82
30. 30.If 2 kites cost ₹16, how much do 9 kites cost? (a) ₹80 (b) ₹72 (c) ₹23 (d) ₹144
31. 31.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 1 day (c) 6 days (d) 5 days
32. 32.If 2 notebooks cost ₹38, how much do 11 notebooks cost? (a) ₹47 (b) ₹209 (c) ₹418 (d) ₹228
33. 33.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹119 (b) ₹85 (c) ₹17 (d) ₹102
34. 34.₹210 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹210 (b) ₹21 (c) ₹189 (d) ₹105
35. 35.If 4 notebooks cost ₹88, how much do 2 notebooks cost? (a) ₹176 (b) ₹44 (c) ₹66 (d) ₹86
36. 36.₹147 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹127 (b) ₹21 (c) ₹147 (d) ₹126
37. 37.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 1 day (d) 2 days
38. 38.If 5 kites cost ₹15, how much do 4 kites cost? (a) ₹14 (b) ₹12 (c) ₹15 (d) ₹60
39. 39.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 4 days (d) 5 days
40. 40.If 7 notebooks cost ₹28, how much do 10 notebooks cost? (a) ₹40 (b) ₹31 (c) ₹280 (d) ₹44

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