Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 675 · 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 14 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 56 days (c) 20 days (d) 57 days
2. 2.If 3 mangoes cost ₹60, how much do 9 mangoes cost? (a) ₹66 (b) ₹540 (c) ₹200 (d) ₹180
3. 3.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 2 days (c) 12 days (d) 18 days
4. 4.If 3 mangoes cost ₹72, how much do 5 mangoes cost? (a) ₹120 (b) ₹144 (c) ₹74 (d) ₹360
5. 5.If 3 kites cost ₹75, how much do 10 kites cost? (a) ₹82 (b) ₹750 (c) ₹275 (d) ₹250
6. 6.₹18 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹12 (b) ₹18 (c) ₹9 (d) ₹6
7. 7.If 2 kites cost ₹38, how much do 3 kites cost? (a) ₹76 (b) ₹39 (c) ₹114 (d) ₹57
8. 8.If 5 kites cost ₹75, how much do 7 kites cost? (a) ₹120 (b) ₹105 (c) ₹77 (d) ₹525
9. 9.If 8 kites cost ₹152, how much do 2 kites cost? (a) ₹38 (b) ₹146 (c) ₹57 (d) ₹304
10. 10.If 6 notebooks cost ₹138, how much do 2 notebooks cost? (a) ₹46 (b) ₹276 (c) ₹69 (d) ₹134
11. 11.₹68 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹68 (b) ₹34 (c) ₹51 (d) ₹17
12. 12.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 11 days (b) 6 days (c) 4 days (d) 5 days
13. 13.₹637 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹392 (b) ₹49 (c) ₹441 (d) ₹245
14. 14.If 7 pens cost ₹161, how much do 11 pens cost? (a) ₹253 (b) ₹1771 (c) ₹276 (d) ₹165
15. 15.₹500 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹500 (b) ₹450 (c) ₹50 (d) ₹250
16. 16.3 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
17. 17.If 9 notebooks cost ₹63, how much do 7 notebooks cost? (a) ₹56 (b) ₹61 (c) ₹49 (d) ₹441
18. 18.₹532 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹266 (b) ₹190 (c) ₹342 (d) ₹38
19. 19.If 2 pens cost ₹36, how much do 4 pens cost? (a) ₹144 (b) ₹38 (c) ₹90 (d) ₹72
20. 20.If 9 notebooks cost ₹162, how much do 5 notebooks cost? (a) ₹108 (b) ₹810 (c) ₹158 (d) ₹90
21. 21.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 10 days (d) 3 days
22. 22.If 2 mangoes cost ₹12, how much do 4 mangoes cost? (a) ₹48 (b) ₹30 (c) ₹24 (d) ₹14
23. 23.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 19 days (c) 7 days (d) 39 days
24. 24.If 3 notebooks cost ₹69, how much do 12 notebooks cost? (a) ₹828 (b) ₹78 (c) ₹276 (d) ₹299
25. 25.₹117 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹105 (b) ₹117 (c) ₹104 (d) ₹13
26. 26.If 4 mangoes cost ₹76, how much do 3 mangoes cost? (a) ₹76 (b) ₹57 (c) ₹228 (d) ₹75
27. 27.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 1 day (c) 11 days (d) 3 days
28. 28.If 3 pens cost ₹30, how much do 8 pens cost? (a) ₹240 (b) ₹35 (c) ₹90 (d) ₹80
29. 29.If 9 pens cost ₹36, how much do 10 pens cost? (a) ₹44 (b) ₹37 (c) ₹40 (d) ₹360
30. 30.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 16 days (c) 1 day (d) 13 days
31. 31.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 15 days (d) 6 days
32. 32.If 6 pens cost ₹24, how much do 7 pens cost? (a) ₹168 (b) ₹32 (c) ₹28 (d) ₹25
33. 33.₹470 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹235 (b) ₹141 (c) ₹47 (d) ₹329
34. 34.If 4 kites cost ₹92, how much do 2 kites cost? (a) ₹90 (b) ₹184 (c) ₹46 (d) ₹69
35. 35.₹108 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹12 (b) ₹96 (c) ₹54 (d) ₹108
36. 36.If 3 kites cost ₹39, how much do 5 kites cost? (a) ₹65 (b) ₹195 (c) ₹78 (d) ₹41
37. 37.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 6 days (d) 7 days
38. 38.₹585 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹225 (b) ₹405 (c) ₹360 (d) ₹45
39. 39.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 4 days (d) 7 days
40. 40.₹156 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹78 (b) ₹60 (c) ₹96 (d) ₹12

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