Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 241 · 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 ₹28, how much do 9 pens cost? (a) ₹33 (b) ₹252 (c) ₹70 (d) ₹63
2. 2.₹72 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹42 (b) ₹30 (c) ₹36 (d) ₹6
3. 3.If 7 mangoes cost ₹105, how much do 12 mangoes cost? (a) ₹195 (b) ₹180 (c) ₹1260 (d) ₹110
4. 4.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 5 days (d) 4 days
5. 5.If 3 kites cost ₹63, how much do 12 kites cost? (a) ₹72 (b) ₹273 (c) ₹756 (d) ₹252
6. 6.If 8 pens cost ₹56, how much do 9 pens cost? (a) ₹57 (b) ₹63 (c) ₹70 (d) ₹504
7. 7.₹105 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹105 (b) ₹35 (c) ₹71 (d) ₹70
8. 8.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 34 days (c) 33 days (d) 7 days
9. 9.₹90 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹10 (b) ₹45 (c) ₹90 (d) ₹80
10. 10.If 9 pens cost ₹27, how much do 6 pens cost? (a) ₹162 (b) ₹21 (c) ₹24 (d) ₹18
11. 11.If 4 notebooks cost ₹96, how much do 6 notebooks cost? (a) ₹576 (b) ₹144 (c) ₹98 (d) ₹168
12. 12.If 3 mangoes cost ₹72, how much do 9 mangoes cost? (a) ₹648 (b) ₹240 (c) ₹216 (d) ₹78
13. 13.If 3 notebooks cost ₹66, how much do 9 notebooks cost? (a) ₹72 (b) ₹594 (c) ₹198 (d) ₹220
14. 14.₹377 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹261 (b) ₹29 (c) ₹232 (d) ₹145
15. 15.If 4 mangoes cost ₹80, how much do 10 mangoes cost? (a) ₹800 (b) ₹86 (c) ₹200 (d) ₹220
16. 16.If 9 notebooks cost ₹36, how much do 7 notebooks cost? (a) ₹28 (b) ₹252 (c) ₹32 (d) ₹34
17. 17.₹490 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹245 (b) ₹49 (c) ₹343 (d) ₹147
18. 18.₹160 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹16 (b) ₹144 (c) ₹160 (d) ₹80
19. 19.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 3 days (c) 21 days (d) 11 days
20. 20.If 4 notebooks cost ₹76, how much do 5 notebooks cost? (a) ₹114 (b) ₹95 (c) ₹380 (d) ₹77
21. 21.If 8 mangoes cost ₹104, how much do 2 mangoes cost? (a) ₹208 (b) ₹39 (c) ₹98 (d) ₹26
22. 22.₹423 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹188 (b) ₹47 (c) ₹282 (d) ₹235
23. 23.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 1 day (d) 2 days
24. 24.If 7 mangoes cost ₹112, how much do 10 mangoes cost? (a) ₹115 (b) ₹160 (c) ₹176 (d) ₹1120
25. 25.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 6 days (d) 8 days
26. 26.If 6 pens cost ₹90, how much do 11 pens cost? (a) ₹990 (b) ₹180 (c) ₹165 (d) ₹95
27. 27.₹442 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹272 (b) ₹221 (c) ₹34 (d) ₹170
28. 28.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 17 days (d) 25 days
29. 29.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 45 days (d) 5 days
30. 30.₹130 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹78 (b) ₹65 (c) ₹52 (d) ₹26
31. 31.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 28 days (c) 17 days (d) 7 days
32. 32.₹180 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹90 (b) ₹20 (c) ₹100 (d) ₹80
33. 33.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 3 days (d) 4 days
34. 34.If 9 kites cost ₹36, how much do 2 kites cost? (a) ₹12 (b) ₹8 (c) ₹29 (d) ₹72
35. 35.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 11 days
36. 36.₹286 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹22 (b) ₹176 (c) ₹110 (d) ₹143
37. 37.₹135 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹75 (b) ₹90 (c) ₹60 (d) ₹15
38. 38.₹280 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹196 (b) ₹28 (c) ₹84 (d) ₹140
39. 39.₹108 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹108 (b) ₹27 (c) ₹54 (d) ₹81
40. 40.If 9 kites cost ₹108, how much do 10 kites cost? (a) ₹120 (b) ₹1080 (c) ₹132 (d) ₹109

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