Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 863 · 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.If 2 notebooks cost ₹14, how much do 3 notebooks cost? (a) ₹21 (b) ₹28 (c) ₹15 (d) ₹42
2. 2.₹616 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹308 (b) ₹396 (c) ₹220 (d) ₹44
3. 3.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 22 days (d) 23 days
4. 4.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 4 days (d) 13 days
5. 5.₹56 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹42 (b) ₹28 (c) ₹14 (d) ₹56
6. 6.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 19 days (c) 49 days (d) 4 days
7. 7.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 13 days (d) 18 days
8. 8.If 5 notebooks cost ₹60, how much do 4 notebooks cost? (a) ₹60 (b) ₹59 (c) ₹240 (d) ₹48
9. 9.If 7 kites cost ₹91, how much do 2 kites cost? (a) ₹86 (b) ₹26 (c) ₹39 (d) ₹182
10. 10.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 17 days (d) 13 days
11. 11.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 7 days (d) 6 days
12. 12.If 6 mangoes cost ₹96, how much do 10 mangoes cost? (a) ₹100 (b) ₹160 (c) ₹176 (d) ₹960
13. 13.If 4 kites cost ₹76, how much do 7 kites cost? (a) ₹152 (b) ₹79 (c) ₹532 (d) ₹133
14. 14.If 4 notebooks cost ₹80, how much do 7 notebooks cost? (a) ₹83 (b) ₹560 (c) ₹140 (d) ₹160
15. 15.₹140 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹42 (b) ₹70 (c) ₹98 (d) ₹14
16. 16.If 3 notebooks cost ₹15, how much do 5 notebooks cost? (a) ₹17 (b) ₹75 (c) ₹25 (d) ₹30
17. 17.₹260 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹130 (b) ₹180 (c) ₹20 (d) ₹80
18. 18.If 6 pens cost ₹84, how much do 7 pens cost? (a) ₹588 (b) ₹112 (c) ₹98 (d) ₹85
19. 19.If 4 pens cost ₹28, how much do 10 pens cost? (a) ₹77 (b) ₹280 (c) ₹70 (d) ₹34
20. 20.If 6 pens cost ₹126, how much do 4 pens cost? (a) ₹84 (b) ₹124 (c) ₹105 (d) ₹504
21. 21.If 4 mangoes cost ₹100, how much do 6 mangoes cost? (a) ₹102 (b) ₹600 (c) ₹150 (d) ₹175
22. 22.If 4 mangoes cost ₹20, how much do 2 mangoes cost? (a) ₹18 (b) ₹15 (c) ₹10 (d) ₹40
23. 23.If 8 kites cost ₹40, how much do 2 kites cost? (a) ₹80 (b) ₹34 (c) ₹15 (d) ₹10
24. 24.₹136 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹68 (b) ₹136 (c) ₹34 (d) ₹102
25. 25.₹81 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹9 (b) ₹73 (c) ₹72 (d) ₹81
26. 26.If 4 notebooks cost ₹60, how much do 7 notebooks cost? (a) ₹120 (b) ₹420 (c) ₹105 (d) ₹63
27. 27.₹133 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹19 (b) ₹38 (c) ₹114 (d) ₹95
28. 28.If 6 kites cost ₹42, how much do 7 kites cost? (a) ₹294 (b) ₹56 (c) ₹43 (d) ₹49
29. 29.If 6 kites cost ₹36, how much do 11 kites cost? (a) ₹396 (b) ₹72 (c) ₹41 (d) ₹66
30. 30.₹460 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹138 (b) ₹46 (c) ₹322 (d) ₹230
31. 31.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 5 days (c) 11 days (d) 20 days
32. 32.If 2 pens cost ₹34, how much do 12 pens cost? (a) ₹204 (b) ₹408 (c) ₹44 (d) ₹221
33. 33.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 22 days (c) 23 days (d) 14 days
34. 34.₹460 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹414 (b) ₹230 (c) ₹460 (d) ₹46
35. 35.₹312 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹182 (b) ₹156 (c) ₹26 (d) ₹130
36. 36.₹100 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹25 (b) ₹50 (c) ₹75 (d) ₹100
37. 37.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 39 days (c) 19 days (d) 40 days
38. 38.If 2 pens cost ₹6, how much do 12 pens cost? (a) ₹36 (b) ₹16 (c) ₹72 (d) ₹39
39. 39.₹299 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹230 (b) ₹92 (c) ₹207 (d) ₹23
40. 40.If 2 mangoes cost ₹6, how much do 5 mangoes cost? (a) ₹9 (b) ₹30 (c) ₹18 (d) ₹15

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