Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 174 · 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 9 days. How many days will 9 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 11 days (d) 6 days
2. 2.₹125 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹75 (b) ₹25 (c) ₹50 (d) ₹100
3. 3.If 5 pens cost ₹20, how much do 10 pens cost? (a) ₹44 (b) ₹40 (c) ₹200 (d) ₹25
4. 4.If 9 kites cost ₹153, how much do 8 kites cost? (a) ₹1224 (b) ₹153 (c) ₹136 (d) ₹152
5. 5.If 8 kites cost ₹72, how much do 10 kites cost? (a) ₹74 (b) ₹720 (c) ₹99 (d) ₹90
6. 6.If 7 pens cost ₹126, how much do 9 pens cost? (a) ₹128 (b) ₹162 (c) ₹180 (d) ₹1134
7. 7.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 4 days (d) 3 days
8. 8.₹253 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹207 (b) ₹69 (c) ₹184 (d) ₹23
9. 9.9 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) 34 days (d) 33 days
10. 10.₹312 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹39 (b) ₹195 (c) ₹156 (d) ₹117
11. 11.If 5 kites cost ₹20, how much do 4 kites cost? (a) ₹80 (b) ₹16 (c) ₹19 (d) ₹20
12. 12.7 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) 14 days (d) 15 days
13. 13.₹462 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹42 (b) ₹231 (c) ₹336 (d) ₹126
14. 14.If 3 pens cost ₹27, how much do 7 pens cost? (a) ₹189 (b) ₹31 (c) ₹63 (d) ₹72
15. 15.If 8 pens cost ₹40, how much do 11 pens cost? (a) ₹60 (b) ₹43 (c) ₹440 (d) ₹55
16. 16.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 27 days (d) 28 days
17. 17.If 5 kites cost ₹70, how much do 2 kites cost? (a) ₹67 (b) ₹42 (c) ₹28 (d) ₹140
18. 18.₹672 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹432 (b) ₹336 (c) ₹48 (d) ₹240
19. 19.₹374 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹238 (b) ₹136 (c) ₹187 (d) ₹34
20. 20.If 6 mangoes cost ₹24, how much do 2 mangoes cost? (a) ₹48 (b) ₹12 (c) ₹20 (d) ₹8
21. 21.4 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
22. 22.If 5 kites cost ₹20, how much do 9 kites cost? (a) ₹40 (b) ₹36 (c) ₹24 (d) ₹180
23. 23.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 15 days (c) 7 days (d) 6 days
24. 24.If 4 kites cost ₹20, how much do 5 kites cost? (a) ₹21 (b) ₹30 (c) ₹100 (d) ₹25
25. 25.8 workers can build a wall in 9 days. How many days will 4 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 13 days (d) 5 days
26. 26.If 9 kites cost ₹45, how much do 4 kites cost? (a) ₹180 (b) ₹40 (c) ₹25 (d) ₹20
27. 27.If 3 kites cost ₹51, how much do 11 kites cost? (a) ₹59 (b) ₹187 (c) ₹204 (d) ₹561
28. 28.If 5 mangoes cost ₹35, how much do 4 mangoes cost? (a) ₹34 (b) ₹35 (c) ₹28 (d) ₹140
29. 29.₹546 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹336 (b) ₹273 (c) ₹42 (d) ₹210
30. 30.₹588 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹294 (b) ₹210 (c) ₹378 (d) ₹42
31. 31.If 7 kites cost ₹147, how much do 2 kites cost? (a) ₹42 (b) ₹142 (c) ₹63 (d) ₹294
32. 32.If 3 kites cost ₹60, how much do 4 kites cost? (a) ₹80 (b) ₹240 (c) ₹61 (d) ₹100
33. 33.If 2 notebooks cost ₹50, how much do 11 notebooks cost? (a) ₹275 (b) ₹59 (c) ₹300 (d) ₹550
34. 34.₹286 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹26 (b) ₹78 (c) ₹143 (d) ₹208
35. 35.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 60 days (d) 61 days
36. 36.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 6 days (c) 4 days (d) 10 days
37. 37.₹374 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹34 (b) ₹187 (c) ₹204 (d) ₹170
38. 38.If 9 pens cost ₹225, how much do 5 pens cost? (a) ₹221 (b) ₹150 (c) ₹125 (d) ₹1125
39. 39.₹120 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹120 (b) ₹40 (c) ₹80 (d) ₹60
40. 40.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 5 days

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