Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 692 · 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. 1.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 14 days (c) 9 days (d) 15 days
2. 2.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 1 day (d) 8 days
3. 3.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 12 days (c) 6 days (d) 7 days
4. 4.₹126 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹63 (b) ₹9 (c) ₹45 (d) ₹81
5. 5.4 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 36 days (b) 5 days (c) 4 days (d) 20 days
6. 6.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 26 days (c) 27 days (d) 13 days
7. 7.If 5 kites cost ₹125, how much do 7 kites cost? (a) ₹175 (b) ₹200 (c) ₹127 (d) ₹875
8. 8.₹270 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹27 (b) ₹81 (c) ₹189 (d) ₹135
9. 9.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 26 days (c) 11 days (d) 27 days
10. 10.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 4 days (c) 5 days (d) 6 days
11. 11.If 8 pens cost ₹136, how much do 9 pens cost? (a) ₹1224 (b) ₹153 (c) ₹170 (d) ₹137
12. 12.If 2 mangoes cost ₹42, how much do 4 mangoes cost? (a) ₹105 (b) ₹84 (c) ₹168 (d) ₹44
13. 13.If 7 kites cost ₹42, how much do 2 kites cost? (a) ₹12 (b) ₹37 (c) ₹84 (d) ₹18
14. 14.If 5 pens cost ₹25, how much do 9 pens cost? (a) ₹225 (b) ₹50 (c) ₹45 (d) ₹29
15. 15.7 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) 4 days (d) 49 days
16. 16.If 5 kites cost ₹95, how much do 3 kites cost? (a) ₹57 (b) ₹76 (c) ₹93 (d) ₹285
17. 17.₹90 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹27 (b) ₹63 (c) ₹45 (d) ₹9
18. 18.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 2 days (d) 8 days
19. 19.₹387 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹387 (b) ₹43 (c) ₹344 (d) ₹345
20. 20.₹136 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹136 (b) ₹119 (c) ₹68 (d) ₹17
21. 21.₹560 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹280 (b) ₹360 (c) ₹40 (d) ₹200
22. 22.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 13 days (d) 16 days
23. 23.₹33 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹11 (b) ₹23 (c) ₹22 (d) ₹33
24. 24.If 4 kites cost ₹52, how much do 6 kites cost? (a) ₹91 (b) ₹78 (c) ₹312 (d) ₹54
25. 25.If 4 kites cost ₹40, how much do 9 kites cost? (a) ₹360 (b) ₹45 (c) ₹100 (d) ₹90
26. 26.If 5 pens cost ₹35, how much do 12 pens cost? (a) ₹42 (b) ₹420 (c) ₹84 (d) ₹91
27. 27.If 2 pens cost ₹28, how much do 5 pens cost? (a) ₹84 (b) ₹31 (c) ₹70 (d) ₹140
28. 28.If 8 notebooks cost ₹72, how much do 12 notebooks cost? (a) ₹864 (b) ₹117 (c) ₹76 (d) ₹108
29. 29.If 7 mangoes cost ₹28, how much do 5 mangoes cost? (a) ₹24 (b) ₹140 (c) ₹20 (d) ₹26
30. 30.If 7 pens cost ₹91, how much do 8 pens cost? (a) ₹92 (b) ₹728 (c) ₹117 (d) ₹104
31. 31.If 9 pens cost ₹207, how much do 10 pens cost? (a) ₹230 (b) ₹2070 (c) ₹253 (d) ₹208
32. 32.₹686 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹49 (b) ₹245 (c) ₹343 (d) ₹441
33. 33.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 17 days (c) 15 days (d) 13 days
34. 34.If 4 pens cost ₹56, how much do 5 pens cost? (a) ₹70 (b) ₹57 (c) ₹280 (d) ₹84
35. 35.If 5 kites cost ₹105, how much do 8 kites cost? (a) ₹108 (b) ₹840 (c) ₹168 (d) ₹189
36. 36.₹360 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹225 (b) ₹180 (c) ₹135 (d) ₹45
37. 37.If 5 pens cost ₹30, how much do 4 pens cost? (a) ₹120 (b) ₹24 (c) ₹29 (d) ₹30
38. 38.If 2 notebooks cost ₹26, how much do 6 notebooks cost? (a) ₹30 (b) ₹91 (c) ₹78 (d) ₹156
39. 39.If 5 notebooks cost ₹115, how much do 2 notebooks cost? (a) ₹112 (b) ₹230 (c) ₹69 (d) ₹46
40. 40.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 20 days (c) 8 days (d) 12 days

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