Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 335 · 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.If 7 kites cost ₹21, how much do 12 kites cost? (a) ₹252 (b) ₹36 (c) ₹39 (d) ₹26
2. 2.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 28 days (d) 9 days
3. 3.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 21 days (b) 7 days (c) 9 days (d) 6 days
4. 4.₹170 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹153 (b) ₹170 (c) ₹85 (d) ₹17
5. 5.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 16 days (d) 9 days
6. 6.If 4 pens cost ₹32, how much do 7 pens cost? (a) ₹56 (b) ₹64 (c) ₹224 (d) ₹35
7. 7.If 6 pens cost ₹18, how much do 9 pens cost? (a) ₹162 (b) ₹21 (c) ₹30 (d) ₹27
8. 8.₹363 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹231 (b) ₹198 (c) ₹165 (d) ₹33
9. 9.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 7 days (d) 3 days
10. 10.If 8 pens cost ₹176, how much do 9 pens cost? (a) ₹1584 (b) ₹220 (c) ₹198 (d) ₹177
11. 11.5 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 10 days (d) 13 days
12. 12.If 7 pens cost ₹63, how much do 4 pens cost? (a) ₹60 (b) ₹36 (c) ₹45 (d) ₹252
13. 13.₹114 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹38 (b) ₹114 (c) ₹57 (d) ₹76
14. 14.If 6 mangoes cost ₹96, how much do 4 mangoes cost? (a) ₹94 (b) ₹64 (c) ₹80 (d) ₹384
15. 15.If 8 mangoes cost ₹128, how much do 9 mangoes cost? (a) ₹160 (b) ₹129 (c) ₹144 (d) ₹1152
16. 16.₹225 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹45 (b) ₹180 (c) ₹225 (d) ₹181
17. 17.8 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
18. 18.₹602 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹387 (b) ₹43 (c) ₹215 (d) ₹301
19. 19.6 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
20. 20.If 6 kites cost ₹150, how much do 9 kites cost? (a) ₹250 (b) ₹1350 (c) ₹153 (d) ₹225
21. 21.₹130 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹10 (b) ₹65 (c) ₹80 (d) ₹50
22. 22.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 30 days (b) 31 days (c) 19 days (d) 11 days
23. 23.₹552 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹46 (b) ₹322 (c) ₹230 (d) ₹276
24. 24.₹64 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹32 (b) ₹24 (c) ₹8 (d) ₹40
25. 25.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 9 days
26. 26.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 21 days (d) 45 days
27. 27.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 29 days (c) 3 days (d) 13 days
28. 28.₹44 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹11 (b) ₹44 (c) ₹33 (d) ₹22
29. 29.If 3 kites cost ₹21, how much do 4 kites cost? (a) ₹35 (b) ₹84 (c) ₹28 (d) ₹22
30. 30.9 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 18 days (d) 15 days
31. 31.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 9 days (d) 17 days
32. 32.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 10 days (c) 17 days (d) 1 day
33. 33.₹88 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹44 (b) ₹11 (c) ₹33 (d) ₹55
34. 34.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 6 days (d) 12 days
35. 35.₹120 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹60 (b) ₹120 (c) ₹20 (d) ₹100
36. 36.If 3 pens cost ₹51, how much do 9 pens cost? (a) ₹459 (b) ₹153 (c) ₹170 (d) ₹57
37. 37.If 2 pens cost ₹36, how much do 3 pens cost? (a) ₹37 (b) ₹108 (c) ₹54 (d) ₹72
38. 38.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 5 days (c) 9 days (d) 45 days
39. 39.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 4 days (d) 5 days
40. 40.₹574 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹41 (b) ₹287 (c) ₹205 (d) ₹369

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