Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 179 · 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. 1.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 13 days (d) 10 days
2. 2.If 3 pens cost ₹42, how much do 6 pens cost? (a) ₹84 (b) ₹98 (c) ₹45 (d) ₹252
3. 3.If 7 kites cost ₹77, how much do 4 kites cost? (a) ₹55 (b) ₹44 (c) ₹74 (d) ₹308
4. 4.If 6 kites cost ₹42, how much do 10 kites cost? (a) ₹46 (b) ₹70 (c) ₹77 (d) ₹420
5. 5.₹550 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹450 (b) ₹100 (c) ₹275 (d) ₹50
6. 6.₹559 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹344 (b) ₹43 (c) ₹215 (d) ₹387
7. 7.₹110 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹55 (b) ₹60 (c) ₹10 (d) ₹50
8. 8.₹224 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹144 (b) ₹112 (c) ₹16 (d) ₹80
9. 9.₹70 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹70 (b) ₹35 (c) ₹63 (d) ₹7
10. 10.₹396 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹176 (b) ₹220 (c) ₹44 (d) ₹198
11. 11.₹190 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹171 (b) ₹19 (c) ₹95 (d) ₹190
12. 12.If 8 notebooks cost ₹88, how much do 9 notebooks cost? (a) ₹110 (b) ₹792 (c) ₹99 (d) ₹89
13. 13.If 7 kites cost ₹168, how much do 6 kites cost? (a) ₹167 (b) ₹1008 (c) ₹144 (d) ₹168
14. 14.If 5 mangoes cost ₹105, how much do 7 mangoes cost? (a) ₹107 (b) ₹147 (c) ₹735 (d) ₹168
15. 15.If 2 pens cost ₹40, how much do 6 pens cost? (a) ₹140 (b) ₹120 (c) ₹240 (d) ₹44
16. 16.If 2 kites cost ₹12, how much do 4 kites cost? (a) ₹30 (b) ₹14 (c) ₹24 (d) ₹48
17. 17.If 3 pens cost ₹75, how much do 6 pens cost? (a) ₹450 (b) ₹175 (c) ₹150 (d) ₹78
18. 18.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 40 days (d) 39 days
19. 19.If 8 pens cost ₹80, how much do 9 pens cost? (a) ₹100 (b) ₹90 (c) ₹720 (d) ₹81
20. 20.If 2 notebooks cost ₹32, how much do 11 notebooks cost? (a) ₹41 (b) ₹352 (c) ₹176 (d) ₹192
21. 21.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 9 days (d) 25 days
22. 22.If 6 kites cost ₹138, how much do 2 kites cost? (a) ₹276 (b) ₹46 (c) ₹69 (d) ₹134
23. 23.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 5 days (d) 9 days
24. 24.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 17 days (c) 13 days (d) 11 days
25. 25.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 13 days (d) 20 days
26. 26.If 2 kites cost ₹36, how much do 12 kites cost? (a) ₹234 (b) ₹216 (c) ₹46 (d) ₹432
27. 27.3 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 11 days (d) 16 days
28. 28.3 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) 13 days (d) 21 days
29. 29.If 7 notebooks cost ₹140, how much do 9 notebooks cost? (a) ₹142 (b) ₹1260 (c) ₹180 (d) ₹200
30. 30.If 6 notebooks cost ₹66, how much do 11 notebooks cost? (a) ₹132 (b) ₹121 (c) ₹726 (d) ₹71
31. 31.₹162 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹18 (b) ₹162 (c) ₹144 (d) ₹81
32. 32.If 3 pens cost ₹72, how much do 4 pens cost? (a) ₹96 (b) ₹288 (c) ₹120 (d) ₹73
33. 33.If 5 mangoes cost ₹90, how much do 8 mangoes cost? (a) ₹162 (b) ₹720 (c) ₹144 (d) ₹93
34. 34.If 7 pens cost ₹84, how much do 2 pens cost? (a) ₹36 (b) ₹24 (c) ₹79 (d) ₹168
35. 35.₹264 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹24 (b) ₹144 (c) ₹120 (d) ₹132
36. 36.₹207 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹161 (b) ₹184 (c) ₹46 (d) ₹23
37. 37.₹121 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹11 (b) ₹66 (c) ₹55 (d) ₹77
38. 38.If 8 mangoes cost ₹184, how much do 5 mangoes cost? (a) ₹115 (b) ₹138 (c) ₹920 (d) ₹181
39. 39.₹150 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹60 (b) ₹90 (c) ₹75 (d) ₹30
40. 40.₹340 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹170 (b) ₹34 (c) ₹306 (d) ₹340

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