Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 280 · 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. 1.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 16 days (c) 1 day (d) 10 days
2. 2.₹325 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹125 (b) ₹200 (c) ₹225 (d) ₹25
3. 3.₹147 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹21 (b) ₹126 (c) ₹42 (d) ₹105
4. 4.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 16 days (d) 5 days
5. 5.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 4 days (d) 2 days
6. 6.If 7 kites cost ₹105, how much do 8 kites cost? (a) ₹120 (b) ₹106 (c) ₹840 (d) ₹135
7. 7.If 4 mangoes cost ₹52, how much do 8 mangoes cost? (a) ₹104 (b) ₹117 (c) ₹416 (d) ₹56
8. 8.₹21 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹7 (b) ₹21 (c) ₹15 (d) ₹14
9. 9.₹319 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹145 (b) ₹29 (c) ₹174 (d) ₹203
10. 10.₹385 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹35 (b) ₹245 (c) ₹175 (d) ₹210
11. 11.₹350 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹350 (b) ₹35 (c) ₹315 (d) ₹175
12. 12.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 8 days (d) 11 days
13. 13.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 19 days (d) 2 days
14. 14.If 5 pens cost ₹110, how much do 3 pens cost? (a) ₹330 (b) ₹66 (c) ₹108 (d) ₹88
15. 15.If 5 kites cost ₹85, how much do 2 kites cost? (a) ₹51 (b) ₹170 (c) ₹82 (d) ₹34
16. 16.If 2 notebooks cost ₹26, how much do 4 notebooks cost? (a) ₹104 (b) ₹65 (c) ₹28 (d) ₹52
17. 17.₹77 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹56 (b) ₹7 (c) ₹28 (d) ₹49
18. 18.₹217 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹186 (b) ₹187 (c) ₹217 (d) ₹31
19. 19.If 5 kites cost ₹20, how much do 6 kites cost? (a) ₹120 (b) ₹21 (c) ₹28 (d) ₹24
20. 20.₹156 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹12 (b) ₹96 (c) ₹78 (d) ₹60
21. 21.If 9 mangoes cost ₹162, how much do 6 mangoes cost? (a) ₹126 (b) ₹972 (c) ₹159 (d) ₹108
22. 22.If 2 kites cost ₹14, how much do 10 kites cost? (a) ₹77 (b) ₹70 (c) ₹140 (d) ₹22
23. 23.If 7 mangoes cost ₹112, how much do 2 mangoes cost? (a) ₹32 (b) ₹48 (c) ₹107 (d) ₹224
24. 24.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 40 days (c) 19 days (d) 7 days
25. 25.If 7 mangoes cost ₹63, how much do 9 mangoes cost? (a) ₹81 (b) ₹90 (c) ₹567 (d) ₹65
26. 26.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 13 days (d) 12 days
27. 27.If 5 pens cost ₹95, how much do 11 pens cost? (a) ₹228 (b) ₹1045 (c) ₹101 (d) ₹209
28. 28.If 3 kites cost ₹36, how much do 7 kites cost? (a) ₹40 (b) ₹84 (c) ₹252 (d) ₹96
29. 29.If 3 mangoes cost ₹54, how much do 8 mangoes cost? (a) ₹432 (b) ₹59 (c) ₹144 (d) ₹162
30. 30.If 9 notebooks cost ₹63, how much do 3 notebooks cost? (a) ₹57 (b) ₹21 (c) ₹189 (d) ₹28
31. 31.If 4 pens cost ₹56, how much do 6 pens cost? (a) ₹98 (b) ₹58 (c) ₹84 (d) ₹336
32. 32.If 4 pens cost ₹60, how much do 11 pens cost? (a) ₹67 (b) ₹660 (c) ₹180 (d) ₹165
33. 33.If 7 kites cost ₹126, how much do 4 kites cost? (a) ₹504 (b) ₹123 (c) ₹90 (d) ₹72
34. 34.₹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
35. 35.If 6 kites cost ₹60, how much do 5 kites cost? (a) ₹50 (b) ₹60 (c) ₹300 (d) ₹59
36. 36.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 4 days (d) 17 days
37. 37.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 44 days (c) 5 days (d) 17 days
38. 38.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 25 days (d) 17 days
39. 39.₹252 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹28 (b) ₹112 (c) ₹126 (d) ₹140
40. 40.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 33 days (c) 34 days (d) 15 days

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