Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 318 · 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 kites cost ₹72, how much do 12 kites cost? (a) ₹864 (b) ₹81 (c) ₹288 (d) ₹312
2. 2.₹350 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹105 (b) ₹245 (c) ₹175 (d) ₹35
3. 3.If 9 kites cost ₹45, how much do 11 kites cost? (a) ₹47 (b) ₹495 (c) ₹55 (d) ₹60
4. 4.₹407 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹185 (b) ₹37 (c) ₹222 (d) ₹259
5. 5.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 4 days (d) 7 days
6. 6.If 7 kites cost ₹105, how much do 6 kites cost? (a) ₹630 (b) ₹104 (c) ₹105 (d) ₹90
7. 7.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 7 days (d) 3 days
8. 8.₹42 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹7 (b) ₹42 (c) ₹21 (d) ₹35
9. 9.₹460 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹138 (b) ₹46 (c) ₹230 (d) ₹322
10. 10.₹407 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹296 (b) ₹259 (c) ₹148 (d) ₹37
11. 11.If 2 notebooks cost ₹40, how much do 4 notebooks cost? (a) ₹42 (b) ₹80 (c) ₹160 (d) ₹100
12. 12.If 8 kites cost ₹120, how much do 4 kites cost? (a) ₹60 (b) ₹116 (c) ₹75 (d) ₹480
13. 13.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 40 days (c) 19 days (d) 39 days
14. 14.If 3 pens cost ₹60, how much do 8 pens cost? (a) ₹480 (b) ₹65 (c) ₹180 (d) ₹160
15. 15.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 11 days (c) 20 days (d) 21 days
16. 16.If 5 notebooks cost ₹35, how much do 12 notebooks cost? (a) ₹42 (b) ₹84 (c) ₹420 (d) ₹91
17. 17.₹240 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹30 (b) ₹90 (c) ₹120 (d) ₹150
18. 18.₹576 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹48 (b) ₹288 (c) ₹240 (d) ₹336
19. 19.If 8 pens cost ₹56, how much do 4 pens cost? (a) ₹35 (b) ₹52 (c) ₹224 (d) ₹28
20. 20.₹30 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹15 (b) ₹30 (c) ₹5 (d) ₹25
21. 21.If 3 pens cost ₹36, how much do 5 pens cost? (a) ₹72 (b) ₹180 (c) ₹60 (d) ₹38
22. 22.₹186 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹93 (b) ₹186 (c) ₹31 (d) ₹155
23. 23.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 12 days (c) 7 days (d) 16 days
24. 24.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 13 days (b) 16 days (c) 2 days (d) 1 day
25. 25.₹273 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹84 (b) ₹21 (c) ₹189 (d) ₹210
26. 26.If 3 notebooks cost ₹66, how much do 8 notebooks cost? (a) ₹176 (b) ₹71 (c) ₹528 (d) ₹198
27. 27.If 6 kites cost ₹96, how much do 9 kites cost? (a) ₹864 (b) ₹160 (c) ₹144 (d) ₹99
28. 28.₹280 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹100 (b) ₹140 (c) ₹20 (d) ₹180
29. 29.If 3 pens cost ₹36, how much do 12 pens cost? (a) ₹432 (b) ₹45 (c) ₹156 (d) ₹144
30. 30.If 7 pens cost ₹77, how much do 8 pens cost? (a) ₹616 (b) ₹88 (c) ₹78 (d) ₹99
31. 31.If 7 pens cost ₹133, how much do 6 pens cost? (a) ₹133 (b) ₹114 (c) ₹798 (d) ₹132
32. 32.8 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 14 days (c) 16 days (d) 9 days
33. 33.₹63 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹7 (b) ₹42 (c) ₹28 (d) ₹35
34. 34.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 1 day (d) 2 days
35. 35.₹189 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹162 (b) ₹135 (c) ₹27 (d) ₹54
36. 36.If 9 notebooks cost ₹162, how much do 7 notebooks cost? (a) ₹160 (b) ₹144 (c) ₹126 (d) ₹1134
37. 37.If 6 pens cost ₹42, how much do 7 pens cost? (a) ₹43 (b) ₹56 (c) ₹294 (d) ₹49
38. 38.8 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 12 days (c) 11 days (d) 7 days
39. 39.₹432 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹240 (b) ₹192 (c) ₹48 (d) ₹216
40. 40.If 6 notebooks cost ₹42, how much do 12 notebooks cost? (a) ₹91 (b) ₹84 (c) ₹48 (d) ₹504

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