Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 69 · 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.If 7 notebooks cost ₹21, how much do 9 notebooks cost? (a) ₹30 (b) ₹27 (c) ₹189 (d) ₹23
2. 2.₹480 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹200 (b) ₹40 (c) ₹280 (d) ₹240
3. 3.₹528 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹44 (b) ₹308 (c) ₹220 (d) ₹264
4. 4.If 9 mangoes cost ₹27, how much do 5 mangoes cost? (a) ₹23 (b) ₹18 (c) ₹15 (d) ₹135
5. 5.If 4 notebooks cost ₹32, how much do 5 notebooks cost? (a) ₹48 (b) ₹33 (c) ₹40 (d) ₹160
6. 6.If 5 mangoes cost ₹120, how much do 8 mangoes cost? (a) ₹192 (b) ₹216 (c) ₹123 (d) ₹960
7. 7.If 6 notebooks cost ₹24, how much do 11 notebooks cost? (a) ₹264 (b) ₹48 (c) ₹44 (d) ₹29
8. 8.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 45 days (c) 21 days (d) 9 days
9. 9.6 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 36 days (c) 4 days (d) 16 days
10. 10.If 4 kites cost ₹24, how much do 3 kites cost? (a) ₹23 (b) ₹18 (c) ₹24 (d) ₹72
11. 11.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 15 days (c) 21 days (d) 13 days
12. 12.₹77 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹55 (b) ₹33 (c) ₹11 (d) ₹44
13. 13.₹65 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹45 (b) ₹25 (c) ₹5 (d) ₹40
14. 14.If 9 kites cost ₹126, how much do 10 kites cost? (a) ₹154 (b) ₹140 (c) ₹127 (d) ₹1260
15. 15.₹325 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹225 (b) ₹250 (c) ₹25 (d) ₹100
16. 16.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 13 days (c) 15 days (d) 9 days
17. 17.₹235 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹188 (b) ₹47 (c) ₹141 (d) ₹94
18. 18.₹260 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹160 (b) ₹100 (c) ₹20 (d) ₹130
19. 19.₹360 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹180 (b) ₹45 (c) ₹225 (d) ₹135
20. 20.If 9 notebooks cost ₹72, how much do 2 notebooks cost? (a) ₹24 (b) ₹144 (c) ₹16 (d) ₹65
21. 21.If 3 mangoes cost ₹42, how much do 8 mangoes cost? (a) ₹336 (b) ₹47 (c) ₹126 (d) ₹112
22. 22.₹351 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹108 (b) ₹243 (c) ₹27 (d) ₹270
23. 23.If 9 pens cost ₹126, how much do 4 pens cost? (a) ₹504 (b) ₹70 (c) ₹121 (d) ₹56
24. 24.If 3 pens cost ₹42, how much do 7 pens cost? (a) ₹98 (b) ₹294 (c) ₹46 (d) ₹112
25. 25.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 43 days (b) 42 days (c) 18 days (d) 10 days
26. 26.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 2 days (d) 3 days
27. 27.₹341 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹31 (b) ₹124 (c) ₹217 (d) ₹248
28. 28.If 8 kites cost ₹112, how much do 4 kites cost? (a) ₹448 (b) ₹108 (c) ₹70 (d) ₹56
29. 29.₹54 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹24 (b) ₹6 (c) ₹27 (d) ₹30
30. 30.₹104 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹8 (b) ₹32 (c) ₹72 (d) ₹52
31. 31.If 5 notebooks cost ₹105, how much do 6 notebooks cost? (a) ₹147 (b) ₹126 (c) ₹630 (d) ₹106
32. 32.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 10 days (d) 11 days
33. 33.₹231 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹168 (b) ₹84 (c) ₹147 (d) ₹21
34. 34.If 6 notebooks cost ₹84, how much do 3 notebooks cost? (a) ₹252 (b) ₹42 (c) ₹81 (d) ₹56
35. 35.If 5 notebooks cost ₹60, how much do 6 notebooks cost? (a) ₹72 (b) ₹84 (c) ₹360 (d) ₹61
36. 36.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 14 days (c) 15 days (d) 11 days
37. 37.If 3 mangoes cost ₹18, how much do 8 mangoes cost? (a) ₹144 (b) ₹23 (c) ₹54 (d) ₹48
38. 38.₹119 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹102 (b) ₹17 (c) ₹85 (d) ₹34
39. 39.₹572 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹286 (b) ₹220 (c) ₹44 (d) ₹352
40. 40.If 9 mangoes cost ₹63, how much do 4 mangoes cost? (a) ₹252 (b) ₹28 (c) ₹35 (d) ₹58

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