Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 858 · 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 4 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 8 days (d) 2 days
2. 2.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 17 days (c) 12 days (d) 16 days
3. 3.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 19 days (d) 4 days
4. 4.If 6 kites cost ₹18, how much do 7 kites cost? (a) ₹21 (b) ₹24 (c) ₹19 (d) ₹126
5. 5.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 9 days (c) 22 days (d) 13 days
6. 6.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 18 days (c) 2 days (d) 14 days
7. 7.If 4 pens cost ₹76, how much do 8 pens cost? (a) ₹171 (b) ₹80 (c) ₹608 (d) ₹152
8. 8.If 2 notebooks cost ₹24, how much do 3 notebooks cost? (a) ₹72 (b) ₹48 (c) ₹36 (d) ₹25
9. 9.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 7 days (d) 6 days
10. 10.If 8 pens cost ₹64, how much do 3 pens cost? (a) ₹32 (b) ₹192 (c) ₹59 (d) ₹24
11. 11.If 9 mangoes cost ₹144, how much do 7 mangoes cost? (a) ₹128 (b) ₹1008 (c) ₹142 (d) ₹112
12. 12.₹252 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹180 (b) ₹72 (c) ₹36 (d) ₹126
13. 13.If 8 mangoes cost ₹200, how much do 5 mangoes cost? (a) ₹150 (b) ₹197 (c) ₹1000 (d) ₹125
14. 14.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 13 days (d) 9 days
15. 15.If 3 pens cost ₹21, how much do 11 pens cost? (a) ₹84 (b) ₹231 (c) ₹29 (d) ₹77
16. 16.₹60 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹60 (b) ₹6 (c) ₹54 (d) ₹30
17. 17.₹624 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹384 (b) ₹240 (c) ₹48 (d) ₹312
18. 18.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 36 days (d) 35 days
19. 19.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 7 days (d) 2 days
20. 20.₹91 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹13 (b) ₹65 (c) ₹26 (d) ₹78
21. 21.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 25 days (d) 9 days
22. 22.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 11 days
23. 23.If 4 kites cost ₹36, how much do 7 kites cost? (a) ₹63 (b) ₹72 (c) ₹39 (d) ₹252
24. 24.If 8 pens cost ₹160, how much do 9 pens cost? (a) ₹180 (b) ₹1440 (c) ₹200 (d) ₹161
25. 25.₹56 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹28 (b) ₹16 (c) ₹8 (d) ₹40
26. 26.9 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 16 days (d) 15 days
27. 27.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 12 days
28. 28.₹261 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹145 (b) ₹174 (c) ₹116 (d) ₹29
29. 29.₹611 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹423 (b) ₹235 (c) ₹47 (d) ₹376
30. 30.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 13 days (d) 27 days
31. 31.If 4 kites cost ₹48, how much do 5 kites cost? (a) ₹49 (b) ₹60 (c) ₹72 (d) ₹240
32. 32.₹231 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹126 (b) ₹21 (c) ₹147 (d) ₹105
33. 33.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 8 days (d) 2 days
34. 34.3 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 21 days (b) 48 days (c) 4 days (d) 3 days
35. 35.₹145 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹116 (b) ₹117 (c) ₹145 (d) ₹29
36. 36.If 7 notebooks cost ₹126, how much do 8 notebooks cost? (a) ₹127 (b) ₹162 (c) ₹144 (d) ₹1008
37. 37.₹286 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹198 (b) ₹22 (c) ₹88 (d) ₹143
38. 38.₹188 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹47 (b) ₹188 (c) ₹94 (d) ₹141
39. 39.If 8 mangoes cost ₹152, how much do 4 mangoes cost? (a) ₹95 (b) ₹608 (c) ₹76 (d) ₹148
40. 40.If 5 kites cost ₹35, how much do 11 kites cost? (a) ₹385 (b) ₹84 (c) ₹41 (d) ₹77

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