Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 612 · 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.₹85 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹51 (b) ₹17 (c) ₹68 (d) ₹34
2. 2.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 13 days (c) 3 days (d) 27 days
3. 3.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 11 days (d) 4 days
4. 4.If 2 mangoes cost ₹38, how much do 3 mangoes cost? (a) ₹57 (b) ₹39 (c) ₹76 (d) ₹114
5. 5.If 9 notebooks cost ₹36, how much do 3 notebooks cost? (a) ₹16 (b) ₹30 (c) ₹108 (d) ₹12
6. 6.₹36 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹18 (b) ₹24 (c) ₹36 (d) ₹12
7. 7.₹27 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹18 (b) ₹19 (c) ₹27 (d) ₹9
8. 8.If 8 pens cost ₹40, how much do 4 pens cost? (a) ₹36 (b) ₹160 (c) ₹25 (d) ₹20
9. 9.₹165 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹120 (b) ₹45 (c) ₹15 (d) ₹135
10. 10.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 12 days (c) 18 days (d) 2 days
11. 11.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 1 day (c) 10 days (d) 7 days
12. 12.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 8 days (c) 9 days (d) 7 days
13. 13.₹90 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹30 (b) ₹45 (c) ₹60 (d) ₹90
14. 14.If 2 kites cost ₹26, how much do 4 kites cost? (a) ₹28 (b) ₹104 (c) ₹52 (d) ₹65
15. 15.₹215 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹86 (b) ₹172 (c) ₹129 (d) ₹43
16. 16.₹294 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹147 (b) ₹42 (c) ₹252 (d) ₹294
17. 17.₹30 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹12 (b) ₹15 (c) ₹6 (d) ₹18
18. 18.If 2 kites cost ₹42, how much do 10 kites cost? (a) ₹50 (b) ₹210 (c) ₹420 (d) ₹231
19. 19.₹238 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹119 (b) ₹136 (c) ₹34 (d) ₹102
20. 20.₹330 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹150 (b) ₹180 (c) ₹165 (d) ₹30
21. 21.₹432 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹336 (b) ₹96 (c) ₹48 (d) ₹216
22. 22.₹231 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹33 (b) ₹231 (c) ₹198 (d) ₹199
23. 23.If 4 mangoes cost ₹60, how much do 10 mangoes cost? (a) ₹165 (b) ₹150 (c) ₹600 (d) ₹66
24. 24.₹126 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹21 (b) ₹126 (c) ₹105 (d) ₹63
25. 25.If 9 notebooks cost ₹207, how much do 5 notebooks cost? (a) ₹1035 (b) ₹138 (c) ₹203 (d) ₹115
26. 26.If 7 pens cost ₹175, how much do 3 pens cost? (a) ₹525 (b) ₹100 (c) ₹171 (d) ₹75
27. 27.If 9 kites cost ₹45, how much do 8 kites cost? (a) ₹45 (b) ₹360 (c) ₹44 (d) ₹40
28. 28.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 11 days (d) 6 days
29. 29.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 23 days (c) 22 days (d) 9 days
30. 30.If 6 pens cost ₹42, how much do 2 pens cost? (a) ₹38 (b) ₹21 (c) ₹14 (d) ₹84
31. 31.If 5 kites cost ₹45, how much do 8 kites cost? (a) ₹360 (b) ₹72 (c) ₹81 (d) ₹48
32. 32.If 9 pens cost ₹36, how much do 4 pens cost? (a) ₹31 (b) ₹20 (c) ₹16 (d) ₹144
33. 33.₹112 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹14 (b) ₹56 (c) ₹112 (d) ₹98
34. 34.If 7 notebooks cost ₹140, how much do 8 notebooks cost? (a) ₹160 (b) ₹1120 (c) ₹180 (d) ₹141
35. 35.₹286 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹26 (b) ₹78 (c) ₹143 (d) ₹208
36. 36.If 3 notebooks cost ₹48, how much do 7 notebooks cost? (a) ₹52 (b) ₹112 (c) ₹336 (d) ₹128
37. 37.7 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 14 days (c) 13 days (d) 11 days
38. 38.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 1 day (c) 37 days (d) 36 days
39. 39.If 5 pens cost ₹25, how much do 6 pens cost? (a) ₹30 (b) ₹150 (c) ₹26 (d) ₹35
40. 40.If 4 mangoes cost ₹44, how much do 8 mangoes cost? (a) ₹99 (b) ₹352 (c) ₹48 (d) ₹88

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