Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 16 · 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 8 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 2 days (d) 13 days
2. 2.If 9 notebooks cost ₹153, how much do 11 notebooks cost? (a) ₹155 (b) ₹204 (c) ₹187 (d) ₹1683
3. 3.₹260 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹20 (b) ₹80 (c) ₹130 (d) ₹180
4. 4.₹372 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹186 (b) ₹217 (c) ₹31 (d) ₹155
5. 5.If 6 kites cost ₹108, how much do 10 kites cost? (a) ₹112 (b) ₹198 (c) ₹1080 (d) ₹180
6. 6.₹66 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹44 (b) ₹33 (c) ₹66 (d) ₹22
7. 7.₹162 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹18 (b) ₹162 (c) ₹144 (d) ₹81
8. 8.If 9 mangoes cost ₹63, how much do 5 mangoes cost? (a) ₹35 (b) ₹315 (c) ₹42 (d) ₹59
9. 9.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 2 days (c) 4 days (d) 3 days
10. 10.₹225 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹90 (b) ₹135 (c) ₹45 (d) ₹180
11. 11.If 6 notebooks cost ₹150, how much do 4 notebooks cost? (a) ₹148 (b) ₹600 (c) ₹100 (d) ₹125
12. 12.₹200 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹100 (b) ₹200 (c) ₹150 (d) ₹50
13. 13.If 3 mangoes cost ₹54, how much do 10 mangoes cost? (a) ₹61 (b) ₹540 (c) ₹180 (d) ₹198
14. 14.If 7 notebooks cost ₹63, how much do 2 notebooks cost? (a) ₹126 (b) ₹18 (c) ₹58 (d) ₹27
15. 15.₹400 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹350 (b) ₹50 (c) ₹200 (d) ₹400
16. 16.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 18 days (d) 36 days
17. 17.₹117 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹91 (b) ₹26 (c) ₹13 (d) ₹104
18. 18.If 5 notebooks cost ₹75, how much do 7 notebooks cost? (a) ₹120 (b) ₹105 (c) ₹77 (d) ₹525
19. 19.₹132 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹66 (b) ₹77 (c) ₹55 (d) ₹11
20. 20.₹504 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹210 (b) ₹294 (c) ₹42 (d) ₹252
21. 21.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 27 days (d) 26 days
22. 22.If 8 notebooks cost ₹64, how much do 10 notebooks cost? (a) ₹80 (b) ₹640 (c) ₹88 (d) ₹66
23. 23.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 17 days (b) 32 days (c) 2 days (d) 3 days
24. 24.₹195 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹157 (b) ₹39 (c) ₹195 (d) ₹156
25. 25.₹189 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹189 (b) ₹163 (c) ₹162 (d) ₹27
26. 26.If 5 kites cost ₹105, how much do 2 kites cost? (a) ₹210 (b) ₹63 (c) ₹102 (d) ₹42
27. 27.If 2 pens cost ₹30, how much do 9 pens cost? (a) ₹37 (b) ₹150 (c) ₹135 (d) ₹270
28. 28.₹315 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹210 (b) ₹35 (c) ₹140 (d) ₹175
29. 29.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 17 days (c) 39 days (d) 9 days
30. 30.If 9 pens cost ₹117, how much do 4 pens cost? (a) ₹65 (b) ₹112 (c) ₹468 (d) ₹52
31. 31.If 2 kites cost ₹36, how much do 4 kites cost? (a) ₹90 (b) ₹144 (c) ₹72 (d) ₹38
32. 32.₹72 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹36 (b) ₹9 (c) ₹72 (d) ₹63
33. 33.₹45 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹5 (b) ₹41 (c) ₹45 (d) ₹40
34. 34.If 4 mangoes cost ₹20, how much do 7 mangoes cost? (a) ₹23 (b) ₹35 (c) ₹140 (d) ₹40
35. 35.If 4 notebooks cost ₹48, how much do 10 notebooks cost? (a) ₹120 (b) ₹480 (c) ₹132 (d) ₹54
36. 36.₹123 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹83 (b) ₹123 (c) ₹82 (d) ₹41
37. 37.If 7 pens cost ₹112, how much do 2 pens cost? (a) ₹224 (b) ₹48 (c) ₹32 (d) ₹107
38. 38.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 10 days (d) 3 days
39. 39.If 6 pens cost ₹36, how much do 2 pens cost? (a) ₹72 (b) ₹18 (c) ₹32 (d) ₹12
40. 40.₹266 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹266 (b) ₹38 (c) ₹228 (d) ₹133

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