Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 456 · 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. 1.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 2 days (d) 15 days
2. 2.If 6 kites cost ₹66, how much do 10 kites cost? (a) ₹70 (b) ₹110 (c) ₹660 (d) ₹121
3. 3.If 3 pens cost ₹48, how much do 4 pens cost? (a) ₹64 (b) ₹80 (c) ₹192 (d) ₹49
4. 4.If 4 mangoes cost ₹88, how much do 10 mangoes cost? (a) ₹94 (b) ₹242 (c) ₹880 (d) ₹220
5. 5.If 4 pens cost ₹52, how much do 11 pens cost? (a) ₹572 (b) ₹143 (c) ₹59 (d) ₹156
6. 6.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 9 days (d) 6 days
7. 7.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 4 days (d) 3 days
8. 8.If 2 kites cost ₹20, how much do 7 kites cost? (a) ₹140 (b) ₹80 (c) ₹25 (d) ₹70
9. 9.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 12 days (c) 16 days (d) 11 days
10. 10.If 8 mangoes cost ₹160, how much do 9 mangoes cost? (a) ₹1440 (b) ₹180 (c) ₹161 (d) ₹200
11. 11.₹275 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹200 (b) ₹25 (c) ₹75 (d) ₹225
12. 12.₹296 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹148 (b) ₹37 (c) ₹111 (d) ₹185
13. 13.If 2 pens cost ₹12, how much do 10 pens cost? (a) ₹20 (b) ₹66 (c) ₹60 (d) ₹120
14. 14.If 4 notebooks cost ₹36, how much do 3 notebooks cost? (a) ₹108 (b) ₹36 (c) ₹27 (d) ₹35
15. 15.If 3 mangoes cost ₹36, how much do 4 mangoes cost? (a) ₹48 (b) ₹60 (c) ₹144 (d) ₹37
16. 16.₹336 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹28 (b) ₹168 (c) ₹196 (d) ₹140
17. 17.₹171 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹95 (b) ₹76 (c) ₹114 (d) ₹19
18. 18.If 8 mangoes cost ₹96, how much do 9 mangoes cost? (a) ₹97 (b) ₹120 (c) ₹108 (d) ₹864
19. 19.₹192 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹96 (b) ₹72 (c) ₹24 (d) ₹120
20. 20.₹528 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹220 (b) ₹308 (c) ₹264 (d) ₹44
21. 21.If 7 mangoes cost ₹42, how much do 2 mangoes cost? (a) ₹18 (b) ₹84 (c) ₹12 (d) ₹37
22. 22.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 28 days (c) 29 days (d) 16 days
23. 23.₹132 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹99 (b) ₹33 (c) ₹66 (d) ₹132
24. 24.If 4 mangoes cost ₹16, how much do 2 mangoes cost? (a) ₹8 (b) ₹14 (c) ₹32 (d) ₹12
25. 25.₹259 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹37 (b) ₹185 (c) ₹74 (d) ₹222
26. 26.If 2 notebooks cost ₹32, how much do 12 notebooks cost? (a) ₹42 (b) ₹384 (c) ₹208 (d) ₹192
27. 27.If 2 kites cost ₹20, how much do 9 kites cost? (a) ₹180 (b) ₹100 (c) ₹90 (d) ₹27
28. 28.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 8 days (d) 13 days
29. 29.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 2 days (c) 3 days (d) 4 days
30. 30.If 4 mangoes cost ₹28, how much do 5 mangoes cost? (a) ₹140 (b) ₹35 (c) ₹42 (d) ₹29
31. 31.₹410 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹41 (b) ₹287 (c) ₹123 (d) ₹205
32. 32.8 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 16 days (c) 24 days (d) 6 days
33. 33.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 6 days (d) 8 days
34. 34.If 6 pens cost ₹60, how much do 2 pens cost? (a) ₹20 (b) ₹120 (c) ₹30 (d) ₹56
35. 35.₹270 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹189 (b) ₹81 (c) ₹27 (d) ₹135
36. 36.If 7 pens cost ₹105, how much do 8 pens cost? (a) ₹120 (b) ₹840 (c) ₹135 (d) ₹106
37. 37.₹112 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹8 (b) ₹56 (c) ₹40 (d) ₹72
38. 38.If 7 notebooks cost ₹133, how much do 5 notebooks cost? (a) ₹114 (b) ₹131 (c) ₹95 (d) ₹665
39. 39.₹396 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹165 (b) ₹198 (c) ₹33 (d) ₹231
40. 40.₹63 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹42 (b) ₹63 (c) ₹43 (d) ₹21

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