Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 575 · 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. 1.7 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) 29 days (d) 28 days
2. 2.If 4 kites cost ₹40, how much do 12 kites cost? (a) ₹130 (b) ₹120 (c) ₹48 (d) ₹480
3. 3.If 8 kites cost ₹168, how much do 5 kites cost? (a) ₹840 (b) ₹165 (c) ₹105 (d) ₹126
4. 4.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 9 days (c) 13 days (d) 3 days
5. 5.If 2 notebooks cost ₹24, how much do 5 notebooks cost? (a) ₹60 (b) ₹120 (c) ₹72 (d) ₹27
6. 6.₹432 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹216 (b) ₹180 (c) ₹36 (d) ₹252
7. 7.₹504 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹36 (b) ₹252 (c) ₹180 (d) ₹324
8. 8.If 7 notebooks cost ₹98, how much do 2 notebooks cost? (a) ₹28 (b) ₹42 (c) ₹196 (d) ₹93
9. 9.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹7 (b) ₹35 (c) ₹49 (d) ₹42
10. 10.₹80 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹80 (b) ₹60 (c) ₹20 (d) ₹40
11. 11.₹126 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹63 (b) ₹54 (c) ₹18 (d) ₹72
12. 12.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 6 days (d) 8 days
13. 13.₹325 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹125 (b) ₹25 (c) ₹225 (d) ₹200
14. 14.6 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 12 days (c) 10 days (d) 13 days
15. 15.8 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 20 days (c) 5 days (d) 14 days
16. 16.If 3 pens cost ₹45, how much do 6 pens cost? (a) ₹105 (b) ₹90 (c) ₹270 (d) ₹48
17. 17.₹42 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹28 (b) ₹42 (c) ₹14 (d) ₹21
18. 18.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 4 days (c) 36 days (d) 6 days
19. 19.₹30 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹12 (b) ₹6 (c) ₹18 (d) ₹15
20. 20.₹96 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹84 (b) ₹12 (c) ₹48 (d) ₹96
21. 21.₹300 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹210 (b) ₹150 (c) ₹30 (d) ₹90
22. 22.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 10 days (d) 4 days
23. 23.5 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 30 days (c) 9 days (d) 31 days
24. 24.₹378 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹189 (b) ₹378 (c) ₹42 (d) ₹336
25. 25.₹451 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹205 (b) ₹287 (c) ₹246 (d) ₹41
26. 26.If 2 kites cost ₹16, how much do 4 kites cost? (a) ₹40 (b) ₹64 (c) ₹32 (d) ₹18
27. 27.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 7 days (d) 1 day
28. 28.If 8 kites cost ₹64, how much do 11 kites cost? (a) ₹96 (b) ₹88 (c) ₹704 (d) ₹67
29. 29.If 9 pens cost ₹36, how much do 11 pens cost? (a) ₹396 (b) ₹38 (c) ₹44 (d) ₹48
30. 30.If 4 notebooks cost ₹68, how much do 10 notebooks cost? (a) ₹680 (b) ₹74 (c) ₹187 (d) ₹170
31. 31.₹184 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹23 (b) ₹161 (c) ₹92 (d) ₹184
32. 32.If 2 pens cost ₹8, how much do 7 pens cost? (a) ₹56 (b) ₹13 (c) ₹32 (d) ₹28
33. 33.If 7 mangoes cost ₹42, how much do 2 mangoes cost? (a) ₹84 (b) ₹18 (c) ₹37 (d) ₹12
34. 34.₹93 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹31 (b) ₹62 (c) ₹93 (d) ₹63
35. 35.If 3 pens cost ₹63, how much do 7 pens cost? (a) ₹441 (b) ₹147 (c) ₹168 (d) ₹67
36. 36.₹52 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹52 (b) ₹26 (c) ₹13 (d) ₹39
37. 37.If 9 mangoes cost ₹207, how much do 6 mangoes cost? (a) ₹138 (b) ₹161 (c) ₹204 (d) ₹1242
38. 38.If 2 notebooks cost ₹22, how much do 6 notebooks cost? (a) ₹77 (b) ₹132 (c) ₹26 (d) ₹66
39. 39.If 9 kites cost ₹36, how much do 6 kites cost? (a) ₹33 (b) ₹24 (c) ₹28 (d) ₹216
40. 40.₹264 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹168 (b) ₹24 (c) ₹96 (d) ₹132

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