Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 172 · 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 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 19 days
2. 2.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 15 days (c) 14 days (d) 8 days
3. 3.If 7 notebooks cost ₹154, how much do 3 notebooks cost? (a) ₹88 (b) ₹150 (c) ₹66 (d) ₹462
4. 4.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 4 days (d) 5 days
5. 5.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 14 days (d) 16 days
6. 6.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 27 days (c) 17 days (d) 3 days
7. 7.₹147 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹99 (b) ₹49 (c) ₹98 (d) ₹147
8. 8.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 12 days (d) 2 days
9. 9.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 11 days (d) 6 days
10. 10.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 27 days (b) 17 days (c) 26 days (d) 9 days
11. 11.₹390 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹39 (b) ₹390 (c) ₹195 (d) ₹351
12. 12.₹460 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹46 (b) ₹322 (c) ₹230 (d) ₹138
13. 13.If 8 notebooks cost ₹120, how much do 5 notebooks cost? (a) ₹600 (b) ₹90 (c) ₹75 (d) ₹117
14. 14.If 3 pens cost ₹39, how much do 6 pens cost? (a) ₹42 (b) ₹91 (c) ₹234 (d) ₹78
15. 15.₹448 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹224 (b) ₹160 (c) ₹32 (d) ₹288
16. 16.If 8 mangoes cost ₹96, how much do 5 mangoes cost? (a) ₹60 (b) ₹93 (c) ₹72 (d) ₹480
17. 17.If 3 notebooks cost ₹12, how much do 5 notebooks cost? (a) ₹14 (b) ₹24 (c) ₹60 (d) ₹20
18. 18.₹528 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹264 (b) ₹384 (c) ₹48 (d) ₹144
19. 19.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 4 days (c) 3 days (d) 27 days
20. 20.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 19 days (d) 18 days
21. 21.₹45 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹25 (b) ₹30 (c) ₹5 (d) ₹20
22. 22.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 3 days (d) 4 days
23. 23.If 3 pens cost ₹45, how much do 7 pens cost? (a) ₹49 (b) ₹105 (c) ₹120 (d) ₹315
24. 24.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 9 days (c) 15 days (d) 8 days
25. 25.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 1 day (c) 13 days (d) 21 days
26. 26.₹180 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹90 (b) ₹18 (c) ₹162 (d) ₹180
27. 27.If 7 kites cost ₹105, how much do 8 kites cost? (a) ₹106 (b) ₹840 (c) ₹120 (d) ₹135
28. 28.If 8 kites cost ₹96, how much do 4 kites cost? (a) ₹48 (b) ₹384 (c) ₹92 (d) ₹60
29. 29.₹130 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹39 (b) ₹65 (c) ₹13 (d) ₹91
30. 30.₹364 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹182 (b) ₹28 (c) ₹140 (d) ₹224
31. 31.₹507 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹351 (b) ₹390 (c) ₹156 (d) ₹39
32. 32.₹63 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹14 (b) ₹56 (c) ₹49 (d) ₹7
33. 33.If 7 pens cost ₹28, how much do 3 pens cost? (a) ₹24 (b) ₹12 (c) ₹16 (d) ₹84
34. 34.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 13 days (c) 28 days (d) 27 days
35. 35.If 3 mangoes cost ₹63, how much do 2 mangoes cost? (a) ₹42 (b) ₹63 (c) ₹126 (d) ₹62
36. 36.If 2 kites cost ₹14, how much do 10 kites cost? (a) ₹140 (b) ₹22 (c) ₹70 (d) ₹77
37. 37.If 5 kites cost ₹60, how much do 10 kites cost? (a) ₹65 (b) ₹120 (c) ₹600 (d) ₹132
38. 38.If 7 notebooks cost ₹56, how much do 2 notebooks cost? (a) ₹112 (b) ₹51 (c) ₹24 (d) ₹16
39. 39.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 7 days (c) 6 days (d) 8 days
40. 40.₹288 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹144 (b) ₹256 (c) ₹288 (d) ₹32

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