Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 86 · 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. 1.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 64 days (c) 63 days (d) 7 days
2. 2.₹598 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹299 (b) ₹46 (c) ₹230 (d) ₹368
3. 3.If 7 mangoes cost ₹35, how much do 12 mangoes cost? (a) ₹40 (b) ₹60 (c) ₹65 (d) ₹420
4. 4.If 7 pens cost ₹21, how much do 4 pens cost? (a) ₹15 (b) ₹18 (c) ₹84 (d) ₹12
5. 5.₹85 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹17 (b) ₹85 (c) ₹68 (d) ₹69
6. 6.If 8 pens cost ₹24, how much do 12 pens cost? (a) ₹36 (b) ₹288 (c) ₹28 (d) ₹39
7. 7.If 2 kites cost ₹16, how much do 3 kites cost? (a) ₹17 (b) ₹32 (c) ₹24 (d) ₹48
8. 8.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 5 days (c) 3 days (d) 4 days
9. 9.₹135 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹15 (b) ₹105 (c) ₹120 (d) ₹30
10. 10.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 15 days (c) 9 days (d) 14 days
11. 11.If 5 kites cost ₹30, how much do 10 kites cost? (a) ₹300 (b) ₹35 (c) ₹66 (d) ₹60
12. 12.₹80 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹10 (b) ₹40 (c) ₹80 (d) ₹70
13. 13.If 4 mangoes cost ₹40, how much do 9 mangoes cost? (a) ₹90 (b) ₹100 (c) ₹360 (d) ₹45
14. 14.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 13 days (c) 7 days (d) 6 days
15. 15.If 6 kites cost ₹126, how much do 11 kites cost? (a) ₹252 (b) ₹1386 (c) ₹231 (d) ₹131
16. 16.₹98 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹49 (b) ₹28 (c) ₹14 (d) ₹70
17. 17.₹286 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹26 (b) ₹143 (c) ₹208 (d) ₹78
18. 18.₹256 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹160 (b) ₹128 (c) ₹32 (d) ₹96
19. 19.₹170 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹85 (b) ₹51 (c) ₹17 (d) ₹119
20. 20.If 2 kites cost ₹32, how much do 11 kites cost? (a) ₹192 (b) ₹352 (c) ₹41 (d) ₹176
21. 21.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 39 days (d) 40 days
22. 22.If 2 pens cost ₹20, how much do 3 pens cost? (a) ₹40 (b) ₹30 (c) ₹60 (d) ₹21
23. 23.If 4 notebooks cost ₹68, how much do 8 notebooks cost? (a) ₹544 (b) ₹136 (c) ₹72 (d) ₹153
24. 24.₹121 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹44 (b) ₹77 (c) ₹88 (d) ₹11
25. 25.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 10 days (c) 11 days (d) 12 days
26. 26.If 5 notebooks cost ₹100, how much do 6 notebooks cost? (a) ₹140 (b) ₹120 (c) ₹600 (d) ₹101
27. 27.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 13 days (c) 9 days (d) 12 days
28. 28.₹80 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹48 (b) ₹16 (c) ₹40 (d) ₹32
29. 29.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 13 days (b) 2 days (c) 3 days (d) 4 days
30. 30.₹637 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹196 (b) ₹49 (c) ₹441 (d) ₹490
31. 31.If 9 mangoes cost ₹63, how much do 12 mangoes cost? (a) ₹91 (b) ₹66 (c) ₹756 (d) ₹84
32. 32.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 14 days (d) 9 days
33. 33.₹147 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹42 (b) ₹126 (c) ₹21 (d) ₹105
34. 34.₹360 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹180 (b) ₹160 (c) ₹200 (d) ₹40
35. 35.₹418 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹228 (b) ₹190 (c) ₹38 (d) ₹209
36. 36.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 11 days (d) 10 days
37. 37.₹64 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹8 (b) ₹56 (c) ₹32 (d) ₹64
38. 38.If 2 pens cost ₹26, how much do 9 pens cost? (a) ₹130 (b) ₹33 (c) ₹234 (d) ₹117
39. 39.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 10 days (c) 14 days (d) 2 days
40. 40.If 4 notebooks cost ₹68, how much do 12 notebooks cost? (a) ₹816 (b) ₹76 (c) ₹221 (d) ₹204

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