Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 321 · 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. 1.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 1 day (c) 16 days (d) 17 days
2. 2.₹329 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹235 (b) ₹282 (c) ₹94 (d) ₹47
3. 3.₹240 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹150 (b) ₹90 (c) ₹120 (d) ₹30
4. 4.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 10 days (c) 7 days (d) 11 days
5. 5.₹260 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹130 (b) ₹100 (c) ₹160 (d) ₹20
6. 6.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 18 days (b) 4 days (c) 3 days (d) 5 days
7. 7.₹240 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹216 (b) ₹240 (c) ₹24 (d) ₹120
8. 8.If 3 notebooks cost ₹57, how much do 4 notebooks cost? (a) ₹76 (b) ₹58 (c) ₹228 (d) ₹95
9. 9.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 19 days
10. 10.₹98 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹98 (b) ₹14 (c) ₹49 (d) ₹84
11. 11.If 2 pens cost ₹46, how much do 7 pens cost? (a) ₹184 (b) ₹161 (c) ₹51 (d) ₹322
12. 12.If 2 pens cost ₹36, how much do 12 pens cost? (a) ₹46 (b) ₹234 (c) ₹432 (d) ₹216
13. 13.If 5 notebooks cost ₹125, how much do 12 notebooks cost? (a) ₹300 (b) ₹325 (c) ₹1500 (d) ₹132
14. 14.₹171 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹114 (b) ₹19 (c) ₹76 (d) ₹95
15. 15.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 10 days (d) 7 days
16. 16.₹407 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹296 (b) ₹111 (c) ₹333 (d) ₹37
17. 17.If 3 notebooks cost ₹18, how much do 12 notebooks cost? (a) ₹72 (b) ₹216 (c) ₹27 (d) ₹78
18. 18.8 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 13 days (c) 12 days (d) 7 days
19. 19.₹143 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹78 (b) ₹13 (c) ₹91 (d) ₹65
20. 20.₹75 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹30 (b) ₹60 (c) ₹15 (d) ₹45
21. 21.₹108 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹90 (b) ₹108 (c) ₹54 (d) ₹18
22. 22.₹234 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹18 (b) ₹72 (c) ₹162 (d) ₹117
23. 23.₹104 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹104 (b) ₹52 (c) ₹26 (d) ₹78
24. 24.₹27 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹27 (b) ₹18 (c) ₹19 (d) ₹9
25. 25.If 2 mangoes cost ₹14, how much do 5 mangoes cost? (a) ₹70 (b) ₹17 (c) ₹42 (d) ₹35
26. 26.If 2 notebooks cost ₹46, how much do 7 notebooks cost? (a) ₹322 (b) ₹51 (c) ₹184 (d) ₹161
27. 27.If 7 pens cost ₹28, how much do 4 pens cost? (a) ₹16 (b) ₹20 (c) ₹112 (d) ₹25
28. 28.₹156 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹48 (b) ₹108 (c) ₹12 (d) ₹78
29. 29.₹572 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹44 (b) ₹352 (c) ₹286 (d) ₹220
30. 30.₹559 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹43 (b) ₹430 (c) ₹387 (d) ₹172
31. 31.If 3 pens cost ₹27, how much do 8 pens cost? (a) ₹32 (b) ₹81 (c) ₹72 (d) ₹216
32. 32.If 7 mangoes cost ₹175, how much do 8 mangoes cost? (a) ₹225 (b) ₹1400 (c) ₹176 (d) ₹200
33. 33.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 9 days (d) 5 days
34. 34.₹169 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹65 (b) ₹117 (c) ₹13 (d) ₹104
35. 35.₹66 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹6 (b) ₹24 (c) ₹33 (d) ₹42
36. 36.If 6 kites cost ₹108, how much do 7 kites cost? (a) ₹126 (b) ₹756 (c) ₹144 (d) ₹109
37. 37.₹351 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹234 (b) ₹39 (c) ₹156 (d) ₹195
38. 38.₹341 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹217 (b) ₹155 (c) ₹186 (d) ₹31
39. 39.If 9 mangoes cost ₹171, how much do 12 mangoes cost? (a) ₹247 (b) ₹2052 (c) ₹228 (d) ₹174
40. 40.If 4 pens cost ₹40, how much do 11 pens cost? (a) ₹110 (b) ₹440 (c) ₹120 (d) ₹47

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