Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 239 · 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 pens cost ₹56, how much do 8 pens cost? (a) ₹112 (b) ₹60 (c) ₹448 (d) ₹126
2. 2.₹342 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹38 (b) ₹171 (c) ₹266 (d) ₹76
3. 3.₹45 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹9 (b) ₹36 (c) ₹27 (d) ₹18
4. 4.₹84 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹42 (b) ₹30 (c) ₹54 (d) ₹6
5. 5.If 9 pens cost ₹135, how much do 10 pens cost? (a) ₹1350 (b) ₹165 (c) ₹136 (d) ₹150
6. 6.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 7 days (d) 5 days
7. 7.₹65 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹13 (b) ₹65 (c) ₹52 (d) ₹53
8. 8.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 17 days (c) 11 days (d) 18 days
9. 9.₹407 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹111 (b) ₹296 (c) ₹333 (d) ₹37
10. 10.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 6 days (d) 8 days
11. 11.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 4 days (c) 27 days (d) 3 days
12. 12.₹15 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹5 (b) ₹15 (c) ₹11 (d) ₹10
13. 13.₹310 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹93 (b) ₹217 (c) ₹155 (d) ₹31
14. 14.If 3 notebooks cost ₹60, how much do 11 notebooks cost? (a) ₹68 (b) ₹220 (c) ₹240 (d) ₹660
15. 15.₹60 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹60 (b) ₹30 (c) ₹54 (d) ₹6
16. 16.If 2 mangoes cost ₹18, how much do 3 mangoes cost? (a) ₹19 (b) ₹54 (c) ₹36 (d) ₹27
17. 17.₹351 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹195 (b) ₹39 (c) ₹234 (d) ₹156
18. 18.₹184 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹92 (b) ₹23 (c) ₹161 (d) ₹184
19. 19.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 5 days (d) 6 days
20. 20.₹341 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹31 (b) ₹155 (c) ₹186 (d) ₹217
21. 21.₹120 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹10 (b) ₹60 (c) ₹70 (d) ₹50
22. 22.₹220 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹110 (b) ₹22 (c) ₹154 (d) ₹66
23. 23.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 13 days
24. 24.If 6 notebooks cost ₹60, how much do 7 notebooks cost? (a) ₹420 (b) ₹80 (c) ₹70 (d) ₹61
25. 25.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 14 days (c) 7 days (d) 9 days
26. 26.If 8 kites cost ₹40, how much do 4 kites cost? (a) ₹20 (b) ₹36 (c) ₹25 (d) ₹160
27. 27.If 2 kites cost ₹14, how much do 4 kites cost? (a) ₹35 (b) ₹56 (c) ₹28 (d) ₹16
28. 28.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 19 days (c) 9 days (d) 49 days
29. 29.If 2 pens cost ₹32, how much do 7 pens cost? (a) ₹112 (b) ₹37 (c) ₹224 (d) ₹128
30. 30.₹286 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹143 (b) ₹26 (c) ₹156 (d) ₹130
31. 31.If 2 mangoes cost ₹16, how much do 4 mangoes cost? (a) ₹40 (b) ₹64 (c) ₹32 (d) ₹18
32. 32.If 8 notebooks cost ₹104, how much do 4 notebooks cost? (a) ₹100 (b) ₹65 (c) ₹416 (d) ₹52
33. 33.If 3 mangoes cost ₹63, how much do 4 mangoes cost? (a) ₹105 (b) ₹252 (c) ₹64 (d) ₹84
34. 34.If 7 pens cost ₹21, how much do 11 pens cost? (a) ₹33 (b) ₹231 (c) ₹25 (d) ₹36
35. 35.₹171 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹76 (b) ₹19 (c) ₹114 (d) ₹95
36. 36.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 10 days (c) 16 days (d) 11 days
37. 37.If 5 pens cost ₹30, how much do 10 pens cost? (a) ₹300 (b) ₹35 (c) ₹60 (d) ₹66
38. 38.If 4 pens cost ₹32, how much do 8 pens cost? (a) ₹36 (b) ₹64 (c) ₹256 (d) ₹72
39. 39.If 4 pens cost ₹52, how much do 2 pens cost? (a) ₹50 (b) ₹104 (c) ₹39 (d) ₹26
40. 40.₹378 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹189 (b) ₹210 (c) ₹42 (d) ₹168

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