Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 363 · 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. 1.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 12 days (d) 7 days
2. 2.If 3 kites cost ₹36, how much do 5 kites cost? (a) ₹38 (b) ₹180 (c) ₹72 (d) ₹60
3. 3.If 8 kites cost ₹48, how much do 7 kites cost? (a) ₹48 (b) ₹47 (c) ₹336 (d) ₹42
4. 4.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 21 days (d) 22 days
5. 5.If 3 pens cost ₹33, how much do 8 pens cost? (a) ₹99 (b) ₹38 (c) ₹264 (d) ₹88
6. 6.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 7 days (d) 9 days
7. 7.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 15 days (c) 27 days (d) 3 days
8. 8.₹329 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹235 (b) ₹47 (c) ₹188 (d) ₹141
9. 9.If 6 notebooks cost ₹30, how much do 2 notebooks cost? (a) ₹26 (b) ₹60 (c) ₹10 (d) ₹15
10. 10.₹114 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹114 (b) ₹19 (c) ₹57 (d) ₹95
11. 11.₹434 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹217 (b) ₹155 (c) ₹31 (d) ₹279
12. 12.If 8 mangoes cost ₹168, how much do 11 mangoes cost? (a) ₹1848 (b) ₹231 (c) ₹252 (d) ₹171
13. 13.If 6 mangoes cost ₹150, how much do 4 mangoes cost? (a) ₹100 (b) ₹148 (c) ₹600 (d) ₹125
14. 14.If 8 mangoes cost ₹64, how much do 3 mangoes cost? (a) ₹59 (b) ₹192 (c) ₹32 (d) ₹24
15. 15.₹300 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹30 (b) ₹150 (c) ₹300 (d) ₹270
16. 16.₹341 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹217 (b) ₹248 (c) ₹31 (d) ₹124
17. 17.₹260 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹160 (b) ₹20 (c) ₹100 (d) ₹130
18. 18.₹171 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹95 (b) ₹114 (c) ₹19 (d) ₹76
19. 19.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 4 days (d) 5 days
20. 20.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 1 day
21. 21.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 16 days (d) 10 days
22. 22.If 5 notebooks cost ₹35, how much do 6 notebooks cost? (a) ₹49 (b) ₹42 (c) ₹210 (d) ₹36
23. 23.₹429 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹351 (b) ₹39 (c) ₹117 (d) ₹312
24. 24.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 7 days (d) 18 days
25. 25.If 3 kites cost ₹18, how much do 6 kites cost? (a) ₹36 (b) ₹108 (c) ₹42 (d) ₹21
26. 26.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 2 days (d) 3 days
27. 27.If 2 kites cost ₹34, how much do 7 kites cost? (a) ₹136 (b) ₹119 (c) ₹39 (d) ₹238
28. 28.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 5 days (d) 2 days
29. 29.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 15 days (d) 14 days
30. 30.If 4 mangoes cost ₹52, how much do 12 mangoes cost? (a) ₹60 (b) ₹169 (c) ₹624 (d) ₹156
31. 31.If 2 kites cost ₹10, how much do 7 kites cost? (a) ₹15 (b) ₹40 (c) ₹35 (d) ₹70
32. 32.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 18 days (b) 6 days (c) 14 days (d) 19 days
33. 33.If 6 pens cost ₹108, how much do 4 pens cost? (a) ₹90 (b) ₹106 (c) ₹72 (d) ₹432
34. 34.If 4 notebooks cost ₹76, how much do 6 notebooks cost? (a) ₹78 (b) ₹133 (c) ₹456 (d) ₹114
35. 35.If 4 pens cost ₹28, how much do 3 pens cost? (a) ₹28 (b) ₹84 (c) ₹27 (d) ₹21
36. 36.₹420 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹30 (b) ₹270 (c) ₹150 (d) ₹210
37. 37.If 4 pens cost ₹68, how much do 5 pens cost? (a) ₹85 (b) ₹102 (c) ₹340 (d) ₹69
38. 38.If 8 notebooks cost ₹56, how much do 12 notebooks cost? (a) ₹84 (b) ₹60 (c) ₹91 (d) ₹672
39. 39.If 6 pens cost ₹102, how much do 2 pens cost? (a) ₹204 (b) ₹98 (c) ₹34 (d) ₹51
40. 40.If 5 notebooks cost ₹85, how much do 10 notebooks cost? (a) ₹187 (b) ₹170 (c) ₹850 (d) ₹90

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