Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 67 · 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 2 kites cost ₹36, how much do 9 kites cost? (a) ₹180 (b) ₹43 (c) ₹324 (d) ₹162
2. 2.₹126 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹126 (b) ₹18 (c) ₹63 (d) ₹108
3. 3.₹141 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹95 (b) ₹141 (c) ₹94 (d) ₹47
4. 4.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 7 days (c) 8 days (d) 6 days
5. 5.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 10 days (d) 3 days
6. 6.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 1 day (d) 9 days
7. 7.If 7 mangoes cost ₹112, how much do 9 mangoes cost? (a) ₹1008 (b) ₹160 (c) ₹144 (d) ₹114
8. 8.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 10 days (c) 16 days (d) 1 day
9. 9.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 16 days (c) 14 days (d) 21 days
10. 10.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 13 days (c) 21 days (d) 22 days
11. 11.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹35 (b) ₹42 (c) ₹7 (d) ₹49
12. 12.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 2 days (d) 7 days
13. 13.If 3 mangoes cost ₹51, how much do 4 mangoes cost? (a) ₹204 (b) ₹52 (c) ₹85 (d) ₹68
14. 14.₹480 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹280 (b) ₹240 (c) ₹40 (d) ₹200
15. 15.If 6 notebooks cost ₹150, how much do 10 notebooks cost? (a) ₹154 (b) ₹275 (c) ₹250 (d) ₹1500
16. 16.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 4 days (d) 5 days
17. 17.₹60 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹20 (b) ₹30 (c) ₹40 (d) ₹60
18. 18.If 3 kites cost ₹18, how much do 8 kites cost? (a) ₹23 (b) ₹54 (c) ₹144 (d) ₹48
19. 19.If 6 pens cost ₹150, how much do 8 pens cost? (a) ₹200 (b) ₹1200 (c) ₹152 (d) ₹225
20. 20.If 8 pens cost ₹80, how much do 9 pens cost? (a) ₹81 (b) ₹90 (c) ₹720 (d) ₹100
21. 21.₹456 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹38 (b) ₹266 (c) ₹228 (d) ₹190
22. 22.If 4 notebooks cost ₹96, how much do 7 notebooks cost? (a) ₹672 (b) ₹192 (c) ₹168 (d) ₹99
23. 23.₹135 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹105 (b) ₹30 (c) ₹15 (d) ₹120
24. 24.₹370 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹370 (b) ₹333 (c) ₹185 (d) ₹37
25. 25.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 5 days (c) 15 days (d) 9 days
26. 26.₹476 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹34 (b) ₹170 (c) ₹306 (d) ₹238
27. 27.If 3 pens cost ₹72, how much do 4 pens cost? (a) ₹120 (b) ₹96 (c) ₹73 (d) ₹288
28. 28.3 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 5 days (d) 16 days
29. 29.₹52 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹26 (b) ₹13 (c) ₹52 (d) ₹39
30. 30.₹128 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹128 (b) ₹96 (c) ₹64 (d) ₹32
31. 31.If 5 pens cost ₹95, how much do 3 pens cost? (a) ₹76 (b) ₹285 (c) ₹93 (d) ₹57
32. 32.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 15 days (d) 24 days
33. 33.If 5 notebooks cost ₹110, how much do 12 notebooks cost? (a) ₹1320 (b) ₹264 (c) ₹117 (d) ₹286
34. 34.If 6 pens cost ₹144, how much do 7 pens cost? (a) ₹145 (b) ₹1008 (c) ₹192 (d) ₹168
35. 35.If 4 pens cost ₹16, how much do 9 pens cost? (a) ₹40 (b) ₹144 (c) ₹36 (d) ₹21
36. 36.₹133 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹114 (b) ₹115 (c) ₹19 (d) ₹133
37. 37.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 7 days (d) 4 days
38. 38.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 9 days (c) 15 days (d) 3 days
39. 39.₹180 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹90 (b) ₹180 (c) ₹18 (d) ₹162
40. 40.If 6 mangoes cost ₹78, how much do 10 mangoes cost? (a) ₹82 (b) ₹780 (c) ₹143 (d) ₹130

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