Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 276 · 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 2 workers take, working at the same speed? (a) 18 days (b) 17 days (c) 19 days (d) 11 days
2. 2.₹264 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹132 (b) ₹264 (c) ₹44 (d) ₹220
3. 3.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 13 days (c) 6 days (d) 5 days
4. 4.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 10 days (d) 5 days
5. 5.If 9 notebooks cost ₹63, how much do 7 notebooks cost? (a) ₹61 (b) ₹49 (c) ₹441 (d) ₹56
6. 6.If 9 notebooks cost ₹27, how much do 8 notebooks cost? (a) ₹26 (b) ₹216 (c) ₹27 (d) ₹24
7. 7.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 27 days (c) 28 days (d) 13 days
8. 8.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 5 days (d) 4 days
9. 9.₹360 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹40 (b) ₹200 (c) ₹180 (d) ₹160
10. 10.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 15 days (c) 11 days (d) 27 days
11. 11.If 3 mangoes cost ₹63, how much do 8 mangoes cost? (a) ₹168 (b) ₹68 (c) ₹189 (d) ₹504
12. 12.If 9 kites cost ₹72, how much do 4 kites cost? (a) ₹67 (b) ₹32 (c) ₹40 (d) ₹288
13. 13.If 5 mangoes cost ₹45, how much do 3 mangoes cost? (a) ₹43 (b) ₹36 (c) ₹135 (d) ₹27
14. 14.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 7 days (d) 9 days
15. 15.If 8 pens cost ₹56, how much do 2 pens cost? (a) ₹50 (b) ₹112 (c) ₹14 (d) ₹21
16. 16.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 17 days (d) 13 days
17. 17.₹253 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹184 (b) ₹207 (c) ₹69 (d) ₹23
18. 18.If 8 mangoes cost ₹72, how much do 4 mangoes cost? (a) ₹68 (b) ₹288 (c) ₹45 (d) ₹36
19. 19.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 3 days (d) 4 days
20. 20.₹351 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹273 (b) ₹39 (c) ₹312 (d) ₹78
21. 21.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 12 days (d) 4 days
22. 22.If 4 notebooks cost ₹68, how much do 12 notebooks cost? (a) ₹221 (b) ₹816 (c) ₹204 (d) ₹76
23. 23.If 9 pens cost ₹54, how much do 8 pens cost? (a) ₹54 (b) ₹48 (c) ₹53 (d) ₹432
24. 24.₹297 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹198 (b) ₹132 (c) ₹165 (d) ₹33
25. 25.₹147 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹63 (b) ₹105 (c) ₹21 (d) ₹84
26. 26.₹117 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹78 (b) ₹79 (c) ₹39 (d) ₹117
27. 27.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 8 days (d) 11 days
28. 28.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 3 days (d) 7 days
29. 29.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 12 days (c) 23 days (d) 25 days
30. 30.If 6 notebooks cost ₹138, how much do 5 notebooks cost? (a) ₹115 (b) ₹690 (c) ₹137 (d) ₹138
31. 31.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 25 days (d) 9 days
32. 32.If 7 pens cost ₹147, how much do 6 pens cost? (a) ₹147 (b) ₹126 (c) ₹146 (d) ₹882
33. 33.₹450 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹135 (b) ₹315 (c) ₹45 (d) ₹225
34. 34.₹88 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹33 (b) ₹11 (c) ₹44 (d) ₹55
35. 35.₹66 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹33 (b) ₹6 (c) ₹36 (d) ₹30
36. 36.If 7 kites cost ₹77, how much do 3 kites cost? (a) ₹44 (b) ₹33 (c) ₹73 (d) ₹231
37. 37.₹264 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹99 (b) ₹33 (c) ₹132 (d) ₹165
38. 38.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 21 days (d) 20 days
39. 39.₹378 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹42 (b) ₹210 (c) ₹189 (d) ₹168
40. 40.If 8 mangoes cost ₹144, how much do 3 mangoes cost? (a) ₹139 (b) ₹432 (c) ₹54 (d) ₹72

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