Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 103 · 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.₹112 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹112 (b) ₹84 (c) ₹56 (d) ₹28
2. 2.If 8 kites cost ₹32, how much do 9 kites cost? (a) ₹288 (b) ₹33 (c) ₹40 (d) ₹36
3. 3.If 3 pens cost ₹48, how much do 4 pens cost? (a) ₹80 (b) ₹64 (c) ₹49 (d) ₹192
4. 4.If 5 pens cost ₹20, how much do 4 pens cost? (a) ₹20 (b) ₹16 (c) ₹80 (d) ₹19
5. 5.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 8 days (d) 1 day
6. 6.₹153 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹119 (b) ₹17 (c) ₹136 (d) ₹34
7. 7.₹387 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹387 (b) ₹345 (c) ₹43 (d) ₹344
8. 8.₹165 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹33 (b) ₹133 (c) ₹132 (d) ₹165
9. 9.If 5 mangoes cost ₹25, how much do 11 mangoes cost? (a) ₹55 (b) ₹31 (c) ₹60 (d) ₹275
10. 10.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 7 days (d) 3 days
11. 11.₹644 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹322 (b) ₹414 (c) ₹46 (d) ₹230
12. 12.If 2 kites cost ₹32, how much do 8 kites cost? (a) ₹144 (b) ₹128 (c) ₹256 (d) ₹38
13. 13.If 5 mangoes cost ₹110, how much do 3 mangoes cost? (a) ₹66 (b) ₹108 (c) ₹88 (d) ₹330
14. 14.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 18 days (b) 3 days (c) 2 days (d) 14 days
15. 15.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 7 days
16. 16.If 5 pens cost ₹45, how much do 7 pens cost? (a) ₹72 (b) ₹315 (c) ₹63 (d) ₹47
17. 17.6 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 4 days (c) 8 days (d) 16 days
18. 18.If 4 mangoes cost ₹100, how much do 9 mangoes cost? (a) ₹105 (b) ₹250 (c) ₹900 (d) ₹225
19. 19.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 21 days (d) 17 days
20. 20.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 1 day (d) 11 days
21. 21.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 3 days
22. 22.If 4 kites cost ₹32, how much do 8 kites cost? (a) ₹36 (b) ₹64 (c) ₹256 (d) ₹72
23. 23.If 3 pens cost ₹60, how much do 2 pens cost? (a) ₹60 (b) ₹40 (c) ₹59 (d) ₹120
24. 24.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 16 days (c) 7 days (d) 12 days
25. 25.₹363 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹33 (b) ₹264 (c) ₹99 (d) ₹297
26. 26.If 6 mangoes cost ₹114, how much do 2 mangoes cost? (a) ₹57 (b) ₹38 (c) ₹228 (d) ₹110
27. 27.If 6 mangoes cost ₹78, how much do 4 mangoes cost? (a) ₹52 (b) ₹65 (c) ₹312 (d) ₹76
28. 28.If 7 pens cost ₹147, how much do 6 pens cost? (a) ₹882 (b) ₹146 (c) ₹147 (d) ₹126
29. 29.If 2 pens cost ₹14, how much do 11 pens cost? (a) ₹77 (b) ₹23 (c) ₹84 (d) ₹154
30. 30.₹133 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹76 (b) ₹19 (c) ₹57 (d) ₹95
31. 31.If 4 pens cost ₹100, how much do 6 pens cost? (a) ₹600 (b) ₹102 (c) ₹150 (d) ₹175
32. 32.If 5 pens cost ₹60, how much do 12 pens cost? (a) ₹67 (b) ₹144 (c) ₹156 (d) ₹720
33. 33.If 7 pens cost ₹63, how much do 5 pens cost? (a) ₹315 (b) ₹54 (c) ₹61 (d) ₹45
34. 34.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 28 days (b) 7 days (c) 27 days (d) 17 days
35. 35.6 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 25 days (b) 9 days (c) 11 days (d) 19 days
36. 36.If 3 pens cost ₹30, how much do 4 pens cost? (a) ₹31 (b) ₹120 (c) ₹50 (d) ₹40
37. 37.₹396 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹198 (b) ₹72 (c) ₹36 (d) ₹324
38. 38.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 7 days (d) 6 days
39. 39.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 12 days (c) 6 days (d) 5 days
40. 40.₹369 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹41 (b) ₹82 (c) ₹328 (d) ₹287

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