Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 800 · 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 6 kites cost ₹42, how much do 10 kites cost? (a) ₹420 (b) ₹77 (c) ₹70 (d) ₹46
2. 2.₹209 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹133 (b) ₹19 (c) ₹95 (d) ₹114
3. 3.₹540 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹270 (b) ₹45 (c) ₹225 (d) ₹315
4. 4.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 2 days (d) 6 days
5. 5.If 4 notebooks cost ₹12, how much do 7 notebooks cost? (a) ₹24 (b) ₹15 (c) ₹84 (d) ₹21
6. 6.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 28 days (c) 3 days (d) 27 days
7. 7.If 8 pens cost ₹56, how much do 12 pens cost? (a) ₹672 (b) ₹91 (c) ₹60 (d) ₹84
8. 8.₹192 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹72 (b) ₹96 (c) ₹120 (d) ₹24
9. 9.If 4 kites cost ₹68, how much do 10 kites cost? (a) ₹187 (b) ₹170 (c) ₹680 (d) ₹74
10. 10.If 4 pens cost ₹48, how much do 8 pens cost? (a) ₹52 (b) ₹384 (c) ₹108 (d) ₹96
11. 11.If 9 mangoes cost ₹189, how much do 4 mangoes cost? (a) ₹184 (b) ₹756 (c) ₹84 (d) ₹105
12. 12.₹124 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹124 (b) ₹31 (c) ₹93 (d) ₹62
13. 13.If 2 notebooks cost ₹14, how much do 12 notebooks cost? (a) ₹91 (b) ₹84 (c) ₹24 (d) ₹168
14. 14.If 5 mangoes cost ₹15, how much do 9 mangoes cost? (a) ₹27 (b) ₹30 (c) ₹19 (d) ₹135
15. 15.₹180 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹15 (b) ₹75 (c) ₹90 (d) ₹105
16. 16.If 8 pens cost ₹72, how much do 5 pens cost? (a) ₹45 (b) ₹360 (c) ₹69 (d) ₹54
17. 17.₹442 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹34 (b) ₹170 (c) ₹221 (d) ₹272
18. 18.₹360 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹180 (b) ₹360 (c) ₹320 (d) ₹40
19. 19.If 7 notebooks cost ₹84, how much do 11 notebooks cost? (a) ₹144 (b) ₹132 (c) ₹924 (d) ₹88
20. 20.If 3 kites cost ₹9, how much do 10 kites cost? (a) ₹90 (b) ₹33 (c) ₹30 (d) ₹16
21. 21.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 1 day (d) 10 days
22. 22.₹504 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹294 (b) ₹42 (c) ₹252 (d) ₹210
23. 23.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 7 days
24. 24.₹310 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹31 (b) ₹279 (c) ₹155 (d) ₹310
25. 25.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 28 days (c) 18 days (d) 10 days
26. 26.If 7 kites cost ₹168, how much do 8 kites cost? (a) ₹192 (b) ₹216 (c) ₹1344 (d) ₹169
27. 27.If 8 notebooks cost ₹176, how much do 10 notebooks cost? (a) ₹178 (b) ₹1760 (c) ₹242 (d) ₹220
28. 28.5 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
29. 29.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 23 days (c) 9 days (d) 22 days
30. 30.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 4 days (d) 2 days
31. 31.If 2 notebooks cost ₹6, how much do 10 notebooks cost? (a) ₹60 (b) ₹33 (c) ₹14 (d) ₹30
32. 32.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 18 days (c) 13 days (d) 8 days
33. 33.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 4 days (d) 6 days
34. 34.If 5 pens cost ₹15, how much do 3 pens cost? (a) ₹13 (b) ₹45 (c) ₹12 (d) ₹9
35. 35.₹224 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹140 (b) ₹112 (c) ₹28 (d) ₹84
36. 36.₹220 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹20 (b) ₹110 (c) ₹160 (d) ₹60
37. 37.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 33 days (c) 32 days (d) 14 days
38. 38.If 2 mangoes cost ₹36, how much do 5 mangoes cost? (a) ₹90 (b) ₹108 (c) ₹39 (d) ₹180
39. 39.If 6 pens cost ₹54, how much do 10 pens cost? (a) ₹99 (b) ₹58 (c) ₹90 (d) ₹540
40. 40.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 7 days (d) 1 day

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