Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 44 · 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 ₹18, how much do 9 kites cost? (a) ₹25 (b) ₹90 (c) ₹81 (d) ₹162
2. 2.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 16 days (d) 5 days
3. 3.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 17 days (d) 13 days
4. 4.If 3 kites cost ₹51, how much do 4 kites cost? (a) ₹85 (b) ₹52 (c) ₹68 (d) ₹204
5. 5.If 5 pens cost ₹35, how much do 9 pens cost? (a) ₹63 (b) ₹70 (c) ₹315 (d) ₹39
6. 6.If 4 mangoes cost ₹28, how much do 9 mangoes cost? (a) ₹252 (b) ₹33 (c) ₹70 (d) ₹63
7. 7.₹192 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹96 (b) ₹144 (c) ₹192 (d) ₹48
8. 8.If 3 mangoes cost ₹48, how much do 11 mangoes cost? (a) ₹192 (b) ₹528 (c) ₹176 (d) ₹56
9. 9.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 6 days (c) 9 days (d) 8 days
10. 10.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 18 days (d) 19 days
11. 11.₹341 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹31 (b) ₹279 (c) ₹93 (d) ₹248
12. 12.₹180 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹108 (b) ₹72 (c) ₹36 (d) ₹90
13. 13.If 9 mangoes cost ₹198, how much do 10 mangoes cost? (a) ₹199 (b) ₹1980 (c) ₹242 (d) ₹220
14. 14.₹153 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹17 (b) ₹34 (c) ₹136 (d) ₹119
15. 15.₹259 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹37 (b) ₹259 (c) ₹223 (d) ₹222
16. 16.If 5 kites cost ₹70, how much do 2 kites cost? (a) ₹42 (b) ₹28 (c) ₹67 (d) ₹140
17. 17.₹96 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹12 (b) ₹48 (c) ₹60 (d) ₹36
18. 18.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 3 days (d) 10 days
19. 19.₹396 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹36 (b) ₹198 (c) ₹144 (d) ₹252
20. 20.If 8 mangoes cost ₹24, how much do 10 mangoes cost? (a) ₹30 (b) ₹240 (c) ₹33 (d) ₹26
21. 21.₹232 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹29 (b) ₹203 (c) ₹232 (d) ₹116
22. 22.If 9 mangoes cost ₹189, how much do 10 mangoes cost? (a) ₹210 (b) ₹231 (c) ₹1890 (d) ₹190
23. 23.₹189 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹21 (b) ₹126 (c) ₹84 (d) ₹105
24. 24.₹270 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹135 (b) ₹45 (c) ₹270 (d) ₹225
25. 25.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 7 days (d) 4 days
26. 26.8 workers can build a wall in 9 days. How many days will 4 workers take, working at the same speed? (a) 19 days (b) 5 days (c) 18 days (d) 13 days
27. 27.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 17 days (b) 3 days (c) 1 day (d) 27 days
28. 28.If 8 notebooks cost ₹184, how much do 2 notebooks cost? (a) ₹69 (b) ₹46 (c) ₹368 (d) ₹178
29. 29.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 10 days (d) 9 days
30. 30.₹144 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹144 (b) ₹24 (c) ₹120 (d) ₹72
31. 31.If 9 mangoes cost ₹36, how much do 12 mangoes cost? (a) ₹52 (b) ₹48 (c) ₹39 (d) ₹432
32. 32.₹77 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹28 (b) ₹49 (c) ₹56 (d) ₹7
33. 33.₹351 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹27 (b) ₹108 (c) ₹270 (d) ₹243
34. 34.If 5 kites cost ₹40, how much do 10 kites cost? (a) ₹45 (b) ₹88 (c) ₹400 (d) ₹80
35. 35.₹98 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹49 (b) ₹14 (c) ₹98 (d) ₹84
36. 36.₹564 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹47 (b) ₹329 (c) ₹282 (d) ₹235
37. 37.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 26 days (d) 11 days
38. 38.If 8 pens cost ₹152, how much do 5 pens cost? (a) ₹114 (b) ₹95 (c) ₹760 (d) ₹149
39. 39.If 5 kites cost ₹90, how much do 2 kites cost? (a) ₹54 (b) ₹180 (c) ₹87 (d) ₹36
40. 40.₹112 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹56 (b) ₹42 (c) ₹14 (d) ₹70

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