Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 724 · 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.₹169 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹117 (b) ₹104 (c) ₹13 (d) ₹65
2. 2.₹322 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹23 (b) ₹207 (c) ₹115 (d) ₹161
3. 3.6 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 6 days (d) 10 days
4. 4.If 6 mangoes cost ₹60, how much do 8 mangoes cost? (a) ₹480 (b) ₹90 (c) ₹62 (d) ₹80
5. 5.If 2 kites cost ₹26, how much do 5 kites cost? (a) ₹65 (b) ₹29 (c) ₹78 (d) ₹130
6. 6.₹532 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹342 (b) ₹38 (c) ₹266 (d) ₹190
7. 7.₹130 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹10 (b) ₹50 (c) ₹65 (d) ₹80
8. 8.₹80 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹80 (b) ₹60 (c) ₹20 (d) ₹40
9. 9.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 4 days (d) 5 days
10. 10.If 5 notebooks cost ₹40, how much do 2 notebooks cost? (a) ₹80 (b) ₹37 (c) ₹16 (d) ₹24
11. 11.If 9 pens cost ₹198, how much do 6 pens cost? (a) ₹154 (b) ₹195 (c) ₹1188 (d) ₹132
12. 12.If 3 kites cost ₹27, how much do 10 kites cost? (a) ₹99 (b) ₹270 (c) ₹34 (d) ₹90
13. 13.₹196 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹112 (b) ₹28 (c) ₹98 (d) ₹84
14. 14.If 2 kites cost ₹50, how much do 10 kites cost? (a) ₹250 (b) ₹58 (c) ₹500 (d) ₹275
15. 15.If 9 mangoes cost ₹162, how much do 10 mangoes cost? (a) ₹198 (b) ₹163 (c) ₹1620 (d) ₹180
16. 16.₹484 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹44 (b) ₹242 (c) ₹308 (d) ₹176
17. 17.If 6 pens cost ₹150, how much do 10 pens cost? (a) ₹154 (b) ₹275 (c) ₹250 (d) ₹1500
18. 18.If 4 notebooks cost ₹12, how much do 7 notebooks cost? (a) ₹84 (b) ₹21 (c) ₹24 (d) ₹15
19. 19.If 7 mangoes cost ₹35, how much do 3 mangoes cost? (a) ₹105 (b) ₹31 (c) ₹15 (d) ₹20
20. 20.₹611 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹47 (b) ₹423 (c) ₹235 (d) ₹376
21. 21.If 5 kites cost ₹90, how much do 8 kites cost? (a) ₹93 (b) ₹720 (c) ₹162 (d) ₹144
22. 22.₹35 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹5 (b) ₹30 (c) ₹35 (d) ₹31
23. 23.If 3 pens cost ₹69, how much do 6 pens cost? (a) ₹161 (b) ₹414 (c) ₹138 (d) ₹72
24. 24.If 8 kites cost ₹104, how much do 9 kites cost? (a) ₹936 (b) ₹117 (c) ₹105 (d) ₹130
25. 25.If 9 kites cost ₹225, how much do 11 kites cost? (a) ₹227 (b) ₹2475 (c) ₹275 (d) ₹300
26. 26.₹198 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹198 (b) ₹33 (c) ₹99 (d) ₹165
27. 27.If 7 notebooks cost ₹112, how much do 8 notebooks cost? (a) ₹144 (b) ₹896 (c) ₹128 (d) ₹113
28. 28.If 9 kites cost ₹225, how much do 6 kites cost? (a) ₹222 (b) ₹175 (c) ₹150 (d) ₹1350
29. 29.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 7 days (d) 6 days
30. 30.₹55 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹30 (b) ₹5 (c) ₹35 (d) ₹25
31. 31.If 7 pens cost ₹63, how much do 5 pens cost? (a) ₹315 (b) ₹45 (c) ₹54 (d) ₹61
32. 32.If 7 notebooks cost ₹91, how much do 11 notebooks cost? (a) ₹143 (b) ₹156 (c) ₹95 (d) ₹1001
33. 33.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 6 days (d) 7 days
34. 34.₹324 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹162 (b) ₹36 (c) ₹144 (d) ₹180
35. 35.₹500 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹250 (b) ₹450 (c) ₹50 (d) ₹500
36. 36.If 6 pens cost ₹138, how much do 8 pens cost? (a) ₹140 (b) ₹1104 (c) ₹184 (d) ₹207
37. 37.9 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 5 days (d) 6 days
38. 38.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 17 days (c) 4 days (d) 5 days
39. 39.₹243 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹108 (b) ₹135 (c) ₹162 (d) ₹27
40. 40.If 8 notebooks cost ₹96, how much do 4 notebooks cost? (a) ₹60 (b) ₹92 (c) ₹48 (d) ₹384

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