Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 384 · 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. 1.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 4 days (d) 11 days
2. 2.If 5 notebooks cost ₹65, how much do 12 notebooks cost? (a) ₹156 (b) ₹72 (c) ₹169 (d) ₹780
3. 3.If 2 notebooks cost ₹26, how much do 5 notebooks cost? (a) ₹29 (b) ₹130 (c) ₹65 (d) ₹78
4. 4.₹396 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹220 (b) ₹44 (c) ₹176 (d) ₹198
5. 5.If 3 notebooks cost ₹45, how much do 7 notebooks cost? (a) ₹120 (b) ₹49 (c) ₹105 (d) ₹315
6. 6.₹455 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹280 (b) ₹175 (c) ₹315 (d) ₹35
7. 7.If 6 notebooks cost ₹42, how much do 4 notebooks cost? (a) ₹35 (b) ₹168 (c) ₹28 (d) ₹40
8. 8.If 8 kites cost ₹152, how much do 12 kites cost? (a) ₹1824 (b) ₹228 (c) ₹247 (d) ₹156
9. 9.If 5 kites cost ₹35, how much do 3 kites cost? (a) ₹33 (b) ₹105 (c) ₹28 (d) ₹21
10. 10.₹168 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹168 (b) ₹42 (c) ₹84 (d) ₹126
11. 11.₹156 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹26 (b) ₹156 (c) ₹130 (d) ₹78
12. 12.₹329 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹47 (b) ₹94 (c) ₹282 (d) ₹235
13. 13.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 26 days (c) 27 days (d) 16 days
14. 14.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 7 days (d) 15 days
15. 15.If 5 mangoes cost ₹90, how much do 6 mangoes cost? (a) ₹540 (b) ₹91 (c) ₹126 (d) ₹108
16. 16.If 6 mangoes cost ₹138, how much do 10 mangoes cost? (a) ₹1380 (b) ₹230 (c) ₹253 (d) ₹142
17. 17.If 5 kites cost ₹35, how much do 7 kites cost? (a) ₹245 (b) ₹37 (c) ₹56 (d) ₹49
18. 18.If 8 notebooks cost ₹136, how much do 11 notebooks cost? (a) ₹187 (b) ₹139 (c) ₹204 (d) ₹1496
19. 19.₹72 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹12 (b) ₹72 (c) ₹36 (d) ₹60
20. 20.₹288 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹288 (b) ₹240 (c) ₹48 (d) ₹144
21. 21.₹133 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹19 (b) ₹133 (c) ₹115 (d) ₹114
22. 22.₹42 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹21 (b) ₹6 (c) ₹42 (d) ₹36
23. 23.If 9 notebooks cost ₹54, how much do 7 notebooks cost? (a) ₹48 (b) ₹378 (c) ₹52 (d) ₹42
24. 24.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 9 days (d) 13 days
25. 25.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 15 days (d) 16 days
26. 26.₹195 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹15 (b) ₹135 (c) ₹60 (d) ₹150
27. 27.If 2 notebooks cost ₹28, how much do 10 notebooks cost? (a) ₹36 (b) ₹140 (c) ₹154 (d) ₹280
28. 28.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 28 days (d) 9 days
29. 29.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 42 days (c) 10 days (d) 43 days
30. 30.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 7 days (d) 18 days
31. 31.If 7 pens cost ₹28, how much do 9 pens cost? (a) ₹30 (b) ₹40 (c) ₹252 (d) ₹36
32. 32.If 6 kites cost ₹120, how much do 4 kites cost? (a) ₹80 (b) ₹118 (c) ₹100 (d) ₹480
33. 33.If 7 notebooks cost ₹119, how much do 2 notebooks cost? (a) ₹238 (b) ₹34 (c) ₹114 (d) ₹51
34. 34.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 16 days (d) 10 days
35. 35.₹225 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹25 (b) ₹225 (c) ₹201 (d) ₹200
36. 36.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 4 days (d) 17 days
37. 37.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 13 days (b) 16 days (c) 3 days (d) 4 days
38. 38.If 5 notebooks cost ₹105, how much do 2 notebooks cost? (a) ₹42 (b) ₹210 (c) ₹63 (d) ₹102
39. 39.If 7 pens cost ₹147, how much do 3 pens cost? (a) ₹441 (b) ₹63 (c) ₹84 (d) ₹143
40. 40.₹296 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹111 (b) ₹37 (c) ₹148 (d) ₹185

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