Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 921 · 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.₹72 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹24 (b) ₹48 (c) ₹36 (d) ₹72
2. 2.If 8 notebooks cost ₹24, how much do 7 notebooks cost? (a) ₹168 (b) ₹23 (c) ₹21 (d) ₹24
3. 3.If 2 notebooks cost ₹30, how much do 12 notebooks cost? (a) ₹195 (b) ₹360 (c) ₹180 (d) ₹40
4. 4.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 25 days (c) 17 days (d) 13 days
5. 5.₹448 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹224 (b) ₹160 (c) ₹288 (d) ₹32
6. 6.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 6 days (d) 7 days
7. 7.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 5 days (d) 10 days
8. 8.₹500 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹50 (b) ₹450 (c) ₹500 (d) ₹250
9. 9.₹351 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹195 (b) ₹234 (c) ₹39 (d) ₹156
10. 10.7 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
11. 11.If 6 notebooks cost ₹120, how much do 4 notebooks cost? (a) ₹100 (b) ₹480 (c) ₹80 (d) ₹118
12. 12.If 2 kites cost ₹12, how much do 10 kites cost? (a) ₹120 (b) ₹60 (c) ₹66 (d) ₹20
13. 13.₹50 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹25 (c) ₹10 (d) ₹30
14. 14.₹99 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹18 (b) ₹9 (c) ₹81 (d) ₹90
15. 15.If 7 mangoes cost ₹42, how much do 6 mangoes cost? (a) ₹36 (b) ₹41 (c) ₹42 (d) ₹252
16. 16.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 28 days (b) 18 days (c) 10 days (d) 7 days
17. 17.₹98 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹35 (b) ₹49 (c) ₹63 (d) ₹7
18. 18.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 18 days (c) 19 days (d) 11 days
19. 19.3 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
20. 20.₹175 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹50 (b) ₹150 (c) ₹25 (d) ₹125
21. 21.If 8 notebooks cost ₹144, how much do 3 notebooks cost? (a) ₹72 (b) ₹139 (c) ₹432 (d) ₹54
22. 22.If 3 notebooks cost ₹45, how much do 9 notebooks cost? (a) ₹405 (b) ₹51 (c) ₹150 (d) ₹135
23. 23.If 5 pens cost ₹65, how much do 7 pens cost? (a) ₹104 (b) ₹67 (c) ₹91 (d) ₹455
24. 24.₹312 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹156 (b) ₹273 (c) ₹39 (d) ₹312
25. 25.₹132 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹55 (b) ₹11 (c) ₹66 (d) ₹77
26. 26.₹198 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹99 (b) ₹18 (c) ₹144 (d) ₹54
27. 27.If 4 notebooks cost ₹28, how much do 10 notebooks cost? (a) ₹77 (b) ₹280 (c) ₹70 (d) ₹34
28. 28.₹308 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹198 (b) ₹154 (c) ₹22 (d) ₹110
29. 29.If 3 notebooks cost ₹21, how much do 12 notebooks cost? (a) ₹252 (b) ₹84 (c) ₹30 (d) ₹91
30. 30.6 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 16 days (b) 18 days (c) 14 days (d) 19 days
31. 31.9 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) 11 days (d) 12 days
32. 32.₹686 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹245 (b) ₹343 (c) ₹49 (d) ₹441
33. 33.3 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
34. 34.₹287 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹41 (b) ₹164 (c) ₹123 (d) ₹205
35. 35.₹176 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹144 (b) ₹88 (c) ₹16 (d) ₹32
36. 36.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 18 days (b) 14 days (c) 6 days (d) 19 days
37. 37.If 9 kites cost ₹180, how much do 2 kites cost? (a) ₹40 (b) ₹60 (c) ₹360 (d) ₹173
38. 38.₹279 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹31 (b) ₹124 (c) ₹186 (d) ₹155
39. 39.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 4 days (d) 12 days
40. 40.₹182 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹91 (b) ₹56 (c) ₹126 (d) ₹14

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