Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 919 · 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.₹200 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹20 (b) ₹100 (c) ₹140 (d) ₹60
2. 2.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 6 days (d) 4 days
3. 3.₹170 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹102 (b) ₹34 (c) ₹85 (d) ₹68
4. 4.If 5 kites cost ₹65, how much do 11 kites cost? (a) ₹143 (b) ₹715 (c) ₹156 (d) ₹71
5. 5.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 12 days (d) 5 days
6. 6.₹330 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹180 (b) ₹165 (c) ₹30 (d) ₹150
7. 7.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 12 days
8. 8.If 3 notebooks cost ₹48, how much do 2 notebooks cost? (a) ₹32 (b) ₹47 (c) ₹48 (d) ₹96
9. 9.If 2 kites cost ₹44, how much do 7 kites cost? (a) ₹154 (b) ₹308 (c) ₹49 (d) ₹176
10. 10.If 4 mangoes cost ₹16, how much do 6 mangoes cost? (a) ₹28 (b) ₹24 (c) ₹96 (d) ₹18
11. 11.If 7 pens cost ₹63, how much do 2 pens cost? (a) ₹58 (b) ₹27 (c) ₹18 (d) ₹126
12. 12.If 9 notebooks cost ₹207, how much do 2 notebooks cost? (a) ₹46 (b) ₹200 (c) ₹69 (d) ₹414
13. 13.If 7 kites cost ₹56, how much do 8 kites cost? (a) ₹72 (b) ₹64 (c) ₹448 (d) ₹57
14. 14.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 28 days (c) 7 days (d) 17 days
15. 15.₹301 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹215 (b) ₹129 (c) ₹43 (d) ₹172
16. 16.₹650 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹200 (b) ₹325 (c) ₹50 (d) ₹450
17. 17.₹217 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹93 (b) ₹31 (c) ₹155 (d) ₹124
18. 18.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 9 days (d) 6 days
19. 19.If 3 kites cost ₹42, how much do 12 kites cost? (a) ₹51 (b) ₹182 (c) ₹504 (d) ₹168
20. 20.₹369 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹205 (b) ₹164 (c) ₹246 (d) ₹41
21. 21.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 13 days (d) 10 days
22. 22.₹168 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹14 (b) ₹84 (c) ₹98 (d) ₹70
23. 23.₹336 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹48 (b) ₹168 (c) ₹96 (d) ₹240
24. 24.If 8 mangoes cost ₹80, how much do 3 mangoes cost? (a) ₹75 (b) ₹240 (c) ₹40 (d) ₹30
25. 25.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹40 (b) ₹44 (c) ₹48 (d) ₹8
26. 26.₹175 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹50 (b) ₹125 (c) ₹150 (d) ₹25
27. 27.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 8 days (c) 15 days (d) 9 days
28. 28.₹348 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹174 (b) ₹145 (c) ₹203 (d) ₹29
29. 29.₹75 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹45 (b) ₹30 (c) ₹15 (d) ₹60
30. 30.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 7 days (d) 8 days
31. 31.₹192 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹24 (b) ₹120 (c) ₹96 (d) ₹72
32. 32.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 28 days (c) 19 days (d) 27 days
33. 33.If 4 pens cost ₹20, how much do 3 pens cost? (a) ₹20 (b) ₹15 (c) ₹60 (d) ₹19
34. 34.If 8 pens cost ₹200, how much do 11 pens cost? (a) ₹275 (b) ₹300 (c) ₹203 (d) ₹2200
35. 35.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 10 days (d) 3 days
36. 36.If 3 pens cost ₹75, how much do 4 pens cost? (a) ₹76 (b) ₹300 (c) ₹125 (d) ₹100
37. 37.If 4 kites cost ₹32, how much do 8 kites cost? (a) ₹36 (b) ₹256 (c) ₹72 (d) ₹64
38. 38.₹451 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹328 (b) ₹41 (c) ₹164 (d) ₹287
39. 39.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 24 days (d) 16 days
40. 40.If 3 mangoes cost ₹42, how much do 12 mangoes cost? (a) ₹182 (b) ₹504 (c) ₹168 (d) ₹51

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