Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 163 · 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.₹189 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹105 (b) ₹84 (c) ₹126 (d) ₹21
2. 2.If 3 kites cost ₹21, how much do 4 kites cost? (a) ₹22 (b) ₹84 (c) ₹35 (d) ₹28
3. 3.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 13 days (d) 5 days
4. 4.₹256 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹256 (b) ₹32 (c) ₹224 (d) ₹128
5. 5.₹234 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹117 (b) ₹18 (c) ₹162 (d) ₹72
6. 6.If 3 kites cost ₹60, how much do 12 kites cost? (a) ₹240 (b) ₹69 (c) ₹260 (d) ₹720
7. 7.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 9 days (d) 17 days
8. 8.If 5 kites cost ₹90, how much do 3 kites cost? (a) ₹54 (b) ₹88 (c) ₹270 (d) ₹72
9. 9.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 16 days (c) 13 days (d) 7 days
10. 10.₹462 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹297 (b) ₹231 (c) ₹165 (d) ₹33
11. 11.₹162 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹135 (b) ₹162 (c) ₹81 (d) ₹27
12. 12.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 28 days (b) 18 days (c) 10 days (d) 7 days
13. 13.₹308 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹44 (b) ₹176 (c) ₹132 (d) ₹154
14. 14.₹45 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹9 (b) ₹36 (c) ₹37 (d) ₹45
15. 15.₹209 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹95 (b) ₹133 (c) ₹19 (d) ₹114
16. 16.If 9 mangoes cost ₹117, how much do 11 mangoes cost? (a) ₹119 (b) ₹1287 (c) ₹156 (d) ₹143
17. 17.If 6 mangoes cost ₹120, how much do 8 mangoes cost? (a) ₹960 (b) ₹122 (c) ₹160 (d) ₹180
18. 18.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 9 days (c) 8 days (d) 6 days
19. 19.₹105 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹15 (b) ₹45 (c) ₹75 (d) ₹60
20. 20.If 4 pens cost ₹36, how much do 2 pens cost? (a) ₹34 (b) ₹72 (c) ₹27 (d) ₹18
21. 21.₹507 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹390 (b) ₹39 (c) ₹351 (d) ₹156
22. 22.₹164 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹164 (b) ₹41 (c) ₹82 (d) ₹123
23. 23.₹21 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹15 (b) ₹14 (c) ₹7 (d) ₹21
24. 24.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 13 days (d) 25 days
25. 25.₹319 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹174 (b) ₹29 (c) ₹145 (d) ₹203
26. 26.If 4 notebooks cost ₹56, how much do 8 notebooks cost? (a) ₹60 (b) ₹112 (c) ₹448 (d) ₹126
27. 27.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 9 days (d) 6 days
28. 28.8 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 8 days (c) 6 days (d) 24 days
29. 29.₹224 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹84 (b) ₹140 (c) ₹112 (d) ₹28
30. 30.If 4 pens cost ₹96, how much do 6 pens cost? (a) ₹98 (b) ₹576 (c) ₹168 (d) ₹144
31. 31.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 3 days (d) 2 days
32. 32.₹121 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹110 (b) ₹11 (c) ₹22 (d) ₹99
33. 33.₹423 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹377 (b) ₹376 (c) ₹47 (d) ₹423
34. 34.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 5 days (d) 4 days
35. 35.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 17 days (b) 7 days (c) 11 days (d) 28 days
36. 36.₹75 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹51 (b) ₹50 (c) ₹75 (d) ₹25
37. 37.₹473 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹43 (b) ₹86 (c) ₹387 (d) ₹430
38. 38.₹231 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹66 (b) ₹33 (c) ₹198 (d) ₹165
39. 39.₹90 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹70 (b) ₹10 (c) ₹20 (d) ₹45
40. 40.If 2 kites cost ₹12, how much do 9 kites cost? (a) ₹108 (b) ₹60 (c) ₹54 (d) ₹19

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