Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 397 · 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 4 notebooks cost ₹48, how much do 5 notebooks cost? (a) ₹72 (b) ₹60 (c) ₹240 (d) ₹49
2. 2.If 4 mangoes cost ₹60, how much do 5 mangoes cost? (a) ₹90 (b) ₹75 (c) ₹300 (d) ₹61
3. 3.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 9 days (d) 4 days
4. 4.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 39 days (c) 7 days (d) 19 days
5. 5.₹261 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹29 (b) ₹116 (c) ₹145 (d) ₹174
6. 6.If 7 pens cost ₹21, how much do 5 pens cost? (a) ₹15 (b) ₹19 (c) ₹18 (d) ₹105
7. 7.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 12 days (c) 3 days (d) 10 days
8. 8.If 3 notebooks cost ₹18, how much do 12 notebooks cost? (a) ₹27 (b) ₹216 (c) ₹78 (d) ₹72
9. 9.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹85 (b) ₹102 (c) ₹119 (d) ₹17
10. 10.₹49 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹43 (b) ₹49 (c) ₹42 (d) ₹7
11. 11.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 9 days (d) 10 days
12. 12.If 7 kites cost ₹56, how much do 3 kites cost? (a) ₹32 (b) ₹52 (c) ₹168 (d) ₹24
13. 13.If 2 pens cost ₹16, how much do 11 pens cost? (a) ₹96 (b) ₹176 (c) ₹88 (d) ₹25
14. 14.₹68 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹17 (b) ₹68 (c) ₹51 (d) ₹34
15. 15.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 25 days (b) 9 days (c) 13 days (d) 17 days
16. 16.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 1 day (d) 16 days
17. 17.₹585 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹360 (b) ₹225 (c) ₹45 (d) ₹405
18. 18.If 2 notebooks cost ₹10, how much do 6 notebooks cost? (a) ₹60 (b) ₹14 (c) ₹30 (d) ₹35
19. 19.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 5 days (d) 1 day
20. 20.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 3 days (c) 10 days (d) 2 days
21. 21.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 11 days (d) 9 days
22. 22.If 9 mangoes cost ₹198, how much do 10 mangoes cost? (a) ₹220 (b) ₹199 (c) ₹1980 (d) ₹242
23. 23.If 2 notebooks cost ₹34, how much do 12 notebooks cost? (a) ₹408 (b) ₹44 (c) ₹221 (d) ₹204
24. 24.₹297 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹189 (b) ₹27 (c) ₹135 (d) ₹162
25. 25.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 5 days (c) 4 days (d) 20 days
26. 26.₹414 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹368 (b) ₹46 (c) ₹414 (d) ₹207
27. 27.₹64 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹64 (b) ₹8 (c) ₹56 (d) ₹32
28. 28.₹35 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹25 (b) ₹5 (c) ₹15 (d) ₹20
29. 29.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 25 days (d) 9 days
30. 30.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 3 days (d) 4 days
31. 31.₹121 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹77 (b) ₹44 (c) ₹11 (d) ₹88
32. 32.If 2 mangoes cost ₹42, how much do 11 mangoes cost? (a) ₹51 (b) ₹462 (c) ₹252 (d) ₹231
33. 33.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 16 days (d) 15 days
34. 34.₹184 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹92 (b) ₹115 (c) ₹23 (d) ₹69
35. 35.₹144 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹144 (b) ₹120 (c) ₹72 (d) ₹24
36. 36.If 4 mangoes cost ₹20, how much do 9 mangoes cost? (a) ₹50 (b) ₹45 (c) ₹25 (d) ₹180
37. 37.₹222 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹222 (b) ₹37 (c) ₹111 (d) ₹185
38. 38.₹168 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹84 (b) ₹14 (c) ₹70 (d) ₹98
39. 39.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 10 days (d) 11 days
40. 40.₹66 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹6 (b) ₹24 (c) ₹42 (d) ₹33

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