Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 810 · 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. 1.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 35 days (c) 36 days (d) 5 days
2. 2.If 4 notebooks cost ₹56, how much do 9 notebooks cost? (a) ₹61 (b) ₹140 (c) ₹126 (d) ₹504
3. 3.₹644 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹414 (b) ₹322 (c) ₹230 (d) ₹46
4. 4.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 27 days (d) 28 days
5. 5.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 22 days (c) 23 days (d) 14 days
6. 6.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 2 days (c) 3 days (d) 1 day
7. 7.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 3 days (d) 4 days
8. 8.6 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 12 days (c) 11 days (d) 13 days
9. 9.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 21 days (d) 6 days
10. 10.₹333 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹74 (b) ₹37 (c) ₹296 (d) ₹259
11. 11.If 9 pens cost ₹63, how much do 3 pens cost? (a) ₹57 (b) ₹21 (c) ₹28 (d) ₹189
12. 12.If 4 notebooks cost ₹28, how much do 6 notebooks cost? (a) ₹42 (b) ₹168 (c) ₹30 (d) ₹49
13. 13.₹55 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹5 (b) ₹20 (c) ₹40 (d) ₹35
14. 14.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 15 days (c) 20 days (d) 6 days
15. 15.₹117 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹52 (b) ₹65 (c) ₹13 (d) ₹78
16. 16.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 6 days (d) 5 days
17. 17.₹306 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹34 (b) ₹153 (c) ₹170 (d) ₹136
18. 18.9 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 10 days (d) 9 days
19. 19.If 6 pens cost ₹90, how much do 2 pens cost? (a) ₹180 (b) ₹86 (c) ₹30 (d) ₹45
20. 20.₹121 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹11 (b) ₹22 (c) ₹110 (d) ₹99
21. 21.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 6 days (d) 8 days
22. 22.₹190 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹190 (b) ₹38 (c) ₹95 (d) ₹152
23. 23.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 28 days (b) 11 days (c) 7 days (d) 17 days
24. 24.₹104 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹64 (b) ₹52 (c) ₹40 (d) ₹8
25. 25.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 9 days (d) 11 days
26. 26.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 9 days (d) 5 days
27. 27.If 6 notebooks cost ₹108, how much do 4 notebooks cost? (a) ₹106 (b) ₹432 (c) ₹72 (d) ₹90
28. 28.₹180 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹72 (b) ₹90 (c) ₹36 (d) ₹108
29. 29.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 14 days (c) 15 days (d) 13 days
30. 30.₹39 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹39 (b) ₹27 (c) ₹13 (d) ₹26
31. 31.If 6 pens cost ₹126, how much do 4 pens cost? (a) ₹105 (b) ₹84 (c) ₹504 (d) ₹124
32. 32.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 6 days (c) 7 days (d) 5 days
33. 33.₹60 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹24 (b) ₹36 (c) ₹12 (d) ₹30
34. 34.₹286 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹143 (b) ₹208 (c) ₹78 (d) ₹26
35. 35.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 6 days (c) 5 days (d) 4 days
36. 36.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 9 days (d) 7 days
37. 37.₹81 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹63 (b) ₹18 (c) ₹9 (d) ₹72
38. 38.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 7 days (d) 8 days
39. 39.If 4 kites cost ₹16, how much do 5 kites cost? (a) ₹20 (b) ₹80 (c) ₹17 (d) ₹24
40. 40.If 5 mangoes cost ₹15, how much do 6 mangoes cost? (a) ₹90 (b) ₹18 (c) ₹21 (d) ₹16

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