Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 847 · 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 10 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 7 days (c) 8 days (d) 9 days
2. 2.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 26 days (c) 27 days (d) 15 days
3. 3.If 9 notebooks cost ₹54, how much do 6 notebooks cost? (a) ₹324 (b) ₹51 (c) ₹36 (d) ₹42
4. 4.₹329 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹47 (b) ₹283 (c) ₹282 (d) ₹329
5. 5.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 15 days (c) 13 days (d) 22 days
6. 6.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 15 days (d) 14 days
7. 7.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 15 days (c) 1 day (d) 37 days
8. 8.₹420 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹126 (b) ₹210 (c) ₹294 (d) ₹42
9. 9.₹160 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹80 (b) ₹20 (c) ₹100 (d) ₹60
10. 10.If 8 kites cost ₹184, how much do 10 kites cost? (a) ₹253 (b) ₹1840 (c) ₹230 (d) ₹186
11. 11.If 5 kites cost ₹100, how much do 4 kites cost? (a) ₹99 (b) ₹80 (c) ₹100 (d) ₹400
12. 12.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 11 days (c) 9 days (d) 12 days
13. 13.₹100 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹20 (b) ₹50 (c) ₹100 (d) ₹80
14. 14.If 4 kites cost ₹24, how much do 10 kites cost? (a) ₹30 (b) ₹60 (c) ₹240 (d) ₹66
15. 15.₹352 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹308 (b) ₹352 (c) ₹44 (d) ₹176
16. 16.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 5 days (d) 3 days
17. 17.If 2 kites cost ₹24, how much do 3 kites cost? (a) ₹48 (b) ₹25 (c) ₹36 (d) ₹72
18. 18.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 7 days (d) 4 days
19. 19.If 4 kites cost ₹48, how much do 5 kites cost? (a) ₹49 (b) ₹240 (c) ₹72 (d) ₹60
20. 20.If 8 pens cost ₹72, how much do 10 pens cost? (a) ₹90 (b) ₹74 (c) ₹99 (d) ₹720
21. 21.9 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) 9 days (d) 10 days
22. 22.If 8 kites cost ₹144, how much do 12 kites cost? (a) ₹148 (b) ₹234 (c) ₹1728 (d) ₹216
23. 23.If 7 kites cost ₹28, how much do 5 kites cost? (a) ₹24 (b) ₹140 (c) ₹20 (d) ₹26
24. 24.If 6 notebooks cost ₹144, how much do 3 notebooks cost? (a) ₹141 (b) ₹432 (c) ₹96 (d) ₹72
25. 25.₹215 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹43 (b) ₹129 (c) ₹86 (d) ₹172
26. 26.If 2 notebooks cost ₹14, how much do 7 notebooks cost? (a) ₹56 (b) ₹49 (c) ₹98 (d) ₹19
27. 27.₹234 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹117 (b) ₹72 (c) ₹18 (d) ₹162
28. 28.₹432 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹216 (b) ₹36 (c) ₹252 (d) ₹180
29. 29.₹143 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹91 (b) ₹13 (c) ₹78 (d) ₹65
30. 30.If 5 kites cost ₹15, how much do 8 kites cost? (a) ₹120 (b) ₹24 (c) ₹27 (d) ₹18
31. 31.₹374 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹306 (b) ₹68 (c) ₹34 (d) ₹187
32. 32.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 3 days (d) 5 days
33. 33.If 5 pens cost ₹30, how much do 12 pens cost? (a) ₹72 (b) ₹37 (c) ₹78 (d) ₹360
34. 34.If 8 notebooks cost ₹64, how much do 7 notebooks cost? (a) ₹63 (b) ₹448 (c) ₹56 (d) ₹64
35. 35.₹351 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹195 (b) ₹156 (c) ₹234 (d) ₹39
36. 36.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 7 days (d) 3 days
37. 37.₹195 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹117 (b) ₹78 (c) ₹39 (d) ₹156
38. 38.If 7 kites cost ₹56, how much do 12 kites cost? (a) ₹61 (b) ₹672 (c) ₹104 (d) ₹96
39. 39.If 9 pens cost ₹153, how much do 11 pens cost? (a) ₹1683 (b) ₹187 (c) ₹204 (d) ₹155
40. 40.If 5 notebooks cost ₹85, how much do 6 notebooks cost? (a) ₹510 (b) ₹86 (c) ₹119 (d) ₹102

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