Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 485 · 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.₹377 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹261 (b) ₹116 (c) ₹290 (d) ₹29
2. 2.If 2 pens cost ₹12, how much do 11 pens cost? (a) ₹132 (b) ₹21 (c) ₹72 (d) ₹66
3. 3.If 9 kites cost ₹144, how much do 2 kites cost? (a) ₹48 (b) ₹288 (c) ₹137 (d) ₹32
4. 4.₹182 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹14 (b) ₹126 (c) ₹91 (d) ₹56
5. 5.If 5 kites cost ₹45, how much do 7 kites cost? (a) ₹72 (b) ₹63 (c) ₹315 (d) ₹47
6. 6.₹240 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹100 (b) ₹20 (c) ₹140 (d) ₹120
7. 7.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 1 day (d) 3 days
8. 8.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 4 days (d) 2 days
9. 9.₹114 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹57 (b) ₹76 (c) ₹38 (d) ₹114
10. 10.₹407 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹37 (b) ₹148 (c) ₹259 (d) ₹296
11. 11.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 19 days
12. 12.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 13 days (d) 25 days
13. 13.If 8 notebooks cost ₹184, how much do 4 notebooks cost? (a) ₹92 (b) ₹736 (c) ₹115 (d) ₹180
14. 14.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 15 days (d) 27 days
15. 15.₹144 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹112 (b) ₹72 (c) ₹32 (d) ₹16
16. 16.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 11 days (c) 8 days (d) 13 days
17. 17.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 18 days (c) 3 days (d) 5 days
18. 18.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 28 days (d) 13 days
19. 19.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 6 days (d) 5 days
20. 20.₹250 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹175 (b) ₹125 (c) ₹75 (d) ₹25
21. 21.If 7 notebooks cost ₹77, how much do 8 notebooks cost? (a) ₹78 (b) ₹99 (c) ₹88 (d) ₹616
22. 22.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 10 days (c) 12 days (d) 11 days
23. 23.₹300 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹150 (b) ₹30 (c) ₹270 (d) ₹300
24. 24.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 14 days (d) 15 days
25. 25.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 6 days (d) 12 days
26. 26.9 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 13 days (b) 19 days (c) 3 days (d) 18 days
27. 27.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 4 days (d) 9 days
28. 28.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 3 days (c) 28 days (d) 29 days
29. 29.₹320 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹40 (b) ₹200 (c) ₹120 (d) ₹160
30. 30.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 2 days (c) 13 days (d) 1 day
31. 31.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 28 days (b) 9 days (c) 19 days (d) 7 days
32. 32.₹140 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹70 (b) ₹84 (c) ₹56 (d) ₹28
33. 33.If 8 kites cost ₹56, how much do 6 kites cost? (a) ₹54 (b) ₹49 (c) ₹336 (d) ₹42
34. 34.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 21 days (c) 64 days (d) 63 days
35. 35.₹78 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹54 (b) ₹24 (c) ₹39 (d) ₹6
36. 36.If 2 pens cost ₹30, how much do 5 pens cost? (a) ₹33 (b) ₹150 (c) ₹90 (d) ₹75
37. 37.If 6 pens cost ₹36, how much do 12 pens cost? (a) ₹42 (b) ₹78 (c) ₹72 (d) ₹432
38. 38.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 13 days (b) 8 days (c) 10 days (d) 9 days
39. 39.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 13 days (b) 6 days (c) 5 days (d) 4 days
40. 40.₹190 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹95 (b) ₹76 (c) ₹114 (d) ₹38

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