Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 66 · 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 3 pens cost ₹36, how much do 12 pens cost? (a) ₹144 (b) ₹156 (c) ₹432 (d) ₹45
2. 2.If 8 pens cost ₹160, how much do 11 pens cost? (a) ₹220 (b) ₹163 (c) ₹1760 (d) ₹240
3. 3.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 12 days (d) 8 days
4. 4.If 2 pens cost ₹12, how much do 9 pens cost? (a) ₹60 (b) ₹54 (c) ₹108 (d) ₹19
5. 5.If 2 kites cost ₹24, how much do 4 kites cost? (a) ₹60 (b) ₹48 (c) ₹26 (d) ₹96
6. 6.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 4 days (d) 9 days
7. 7.₹196 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹98 (b) ₹196 (c) ₹147 (d) ₹49
8. 8.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 13 days (d) 25 days
9. 9.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 10 days (c) 6 days (d) 14 days
10. 10.₹304 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹266 (b) ₹152 (c) ₹38 (d) ₹304
11. 11.₹88 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹72 (b) ₹44 (c) ₹16 (d) ₹8
12. 12.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 6 days (d) 7 days
13. 13.If 9 pens cost ₹144, how much do 3 pens cost? (a) ₹64 (b) ₹138 (c) ₹48 (d) ₹432
14. 14.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 5 days (d) 6 days
15. 15.If 5 pens cost ₹20, how much do 10 pens cost? (a) ₹200 (b) ₹44 (c) ₹25 (d) ₹40
16. 16.₹270 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹270 (b) ₹45 (c) ₹135 (d) ₹225
17. 17.If 9 mangoes cost ₹162, how much do 10 mangoes cost? (a) ₹163 (b) ₹180 (c) ₹1620 (d) ₹198
18. 18.If 7 pens cost ₹147, how much do 12 pens cost? (a) ₹152 (b) ₹273 (c) ₹252 (d) ₹1764
19. 19.If 3 kites cost ₹39, how much do 2 kites cost? (a) ₹38 (b) ₹78 (c) ₹26 (d) ₹39
20. 20.If 7 kites cost ₹21, how much do 5 kites cost? (a) ₹15 (b) ₹19 (c) ₹105 (d) ₹18
21. 21.If 9 pens cost ₹54, how much do 5 pens cost? (a) ₹50 (b) ₹36 (c) ₹270 (d) ₹30
22. 22.If 5 mangoes cost ₹120, how much do 3 mangoes cost? (a) ₹96 (b) ₹360 (c) ₹72 (d) ₹118
23. 23.If 4 mangoes cost ₹32, how much do 9 mangoes cost? (a) ₹288 (b) ₹72 (c) ₹37 (d) ₹80
24. 24.If 3 mangoes cost ₹51, how much do 10 mangoes cost? (a) ₹510 (b) ₹58 (c) ₹187 (d) ₹170
25. 25.If 3 pens cost ₹66, how much do 11 pens cost? (a) ₹726 (b) ₹74 (c) ₹242 (d) ₹264
26. 26.If 7 kites cost ₹168, how much do 2 kites cost? (a) ₹336 (b) ₹48 (c) ₹163 (d) ₹72
27. 27.₹81 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹9 (b) ₹45 (c) ₹54 (d) ₹36
28. 28.₹363 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹297 (b) ₹264 (c) ₹33 (d) ₹99
29. 29.If 3 kites cost ₹12, how much do 4 kites cost? (a) ₹48 (b) ₹16 (c) ₹13 (d) ₹20
30. 30.If 5 pens cost ₹40, how much do 7 pens cost? (a) ₹280 (b) ₹64 (c) ₹56 (d) ₹42
31. 31.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 5 days (d) 45 days
32. 32.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 36 days (c) 35 days (d) 19 days
33. 33.₹156 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹78 (b) ₹39 (c) ₹156 (d) ₹117
34. 34.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 16 days (d) 13 days
35. 35.₹110 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹10 (b) ₹50 (c) ₹60 (d) ₹55
36. 36.If 7 kites cost ₹126, how much do 4 kites cost? (a) ₹504 (b) ₹123 (c) ₹72 (d) ₹90
37. 37.₹387 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹258 (b) ₹43 (c) ₹172 (d) ₹215
38. 38.If 8 kites cost ₹56, how much do 12 kites cost? (a) ₹672 (b) ₹91 (c) ₹84 (d) ₹60
39. 39.₹84 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹49 (b) ₹35 (c) ₹7 (d) ₹42
40. 40.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 19 days (c) 20 days (d) 11 days

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