Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 851 · 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 14 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 13 days (c) 15 days (d) 21 days
2. 2.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 31 days (c) 30 days (d) 18 days
3. 3.If 4 mangoes cost ₹52, how much do 7 mangoes cost? (a) ₹104 (b) ₹91 (c) ₹364 (d) ₹55
4. 4.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 27 days (c) 26 days (d) 16 days
5. 5.If 6 pens cost ₹120, how much do 12 pens cost? (a) ₹126 (b) ₹240 (c) ₹1440 (d) ₹260
6. 6.If 6 pens cost ₹84, how much do 4 pens cost? (a) ₹56 (b) ₹70 (c) ₹82 (d) ₹336
7. 7.If 2 mangoes cost ₹30, how much do 3 mangoes cost? (a) ₹60 (b) ₹45 (c) ₹90 (d) ₹31
8. 8.₹221 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹85 (b) ₹17 (c) ₹153 (d) ₹136
9. 9.₹60 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹30 (b) ₹40 (c) ₹60 (d) ₹20
10. 10.If 2 mangoes cost ₹48, how much do 9 mangoes cost? (a) ₹240 (b) ₹216 (c) ₹55 (d) ₹432
11. 11.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 18 days (c) 8 days (d) 13 days
12. 12.If 2 pens cost ₹36, how much do 7 pens cost? (a) ₹252 (b) ₹144 (c) ₹126 (d) ₹41
13. 13.If 8 kites cost ₹184, how much do 2 kites cost? (a) ₹69 (b) ₹368 (c) ₹178 (d) ₹46
14. 14.₹49 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹28 (b) ₹7 (c) ₹35 (d) ₹21
15. 15.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 4 days (d) 10 days
16. 16.If 3 pens cost ₹36, how much do 9 pens cost? (a) ₹324 (b) ₹120 (c) ₹108 (d) ₹42
17. 17.If 4 pens cost ₹16, how much do 5 pens cost? (a) ₹80 (b) ₹20 (c) ₹24 (d) ₹17
18. 18.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 8 days (d) 6 days
19. 19.If 9 pens cost ₹27, how much do 10 pens cost? (a) ₹30 (b) ₹33 (c) ₹28 (d) ₹270
20. 20.If 2 mangoes cost ₹26, how much do 10 mangoes cost? (a) ₹260 (b) ₹34 (c) ₹143 (d) ₹130
21. 21.If 7 pens cost ₹140, how much do 8 pens cost? (a) ₹160 (b) ₹180 (c) ₹141 (d) ₹1120
22. 22.If 9 kites cost ₹63, how much do 7 kites cost? (a) ₹61 (b) ₹49 (c) ₹441 (d) ₹56
23. 23.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 11 days (d) 7 days
24. 24.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 7 days (d) 10 days
25. 25.If 7 pens cost ₹42, how much do 5 pens cost? (a) ₹30 (b) ₹40 (c) ₹36 (d) ₹210
26. 26.₹242 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹22 (b) ₹121 (c) ₹132 (d) ₹110
27. 27.₹35 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹5 (b) ₹10 (c) ₹25 (d) ₹30
28. 28.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 13 days (c) 20 days (d) 7 days
29. 29.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 16 days (d) 12 days
30. 30.If 8 notebooks cost ₹72, how much do 12 notebooks cost? (a) ₹117 (b) ₹864 (c) ₹108 (d) ₹76
31. 31.₹418 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹114 (b) ₹304 (c) ₹38 (d) ₹209
32. 32.₹220 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹110 (b) ₹220 (c) ₹198 (d) ₹22
33. 33.If 5 kites cost ₹110, how much do 7 kites cost? (a) ₹154 (b) ₹770 (c) ₹112 (d) ₹176
34. 34.If 4 kites cost ₹12, how much do 6 kites cost? (a) ₹21 (b) ₹14 (c) ₹18 (d) ₹72
35. 35.If 9 mangoes cost ₹90, how much do 3 mangoes cost? (a) ₹30 (b) ₹270 (c) ₹84 (d) ₹40
36. 36.₹144 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹144 (b) ₹72 (c) ₹126 (d) ₹18
37. 37.If 2 mangoes cost ₹38, how much do 5 mangoes cost? (a) ₹190 (b) ₹41 (c) ₹95 (d) ₹114
38. 38.₹144 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹72 (b) ₹84 (c) ₹12 (d) ₹60
39. 39.If 7 mangoes cost ₹147, how much do 5 mangoes cost? (a) ₹735 (b) ₹145 (c) ₹126 (d) ₹105
40. 40.₹392 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹196 (b) ₹28 (c) ₹252 (d) ₹140

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