Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 685 · 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. 1.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 41 days (b) 4 days (c) 16 days (d) 40 days
2. 2.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 18 days (c) 5 days (d) 4 days
3. 3.₹405 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹45 (b) ₹270 (c) ₹180 (d) ₹225
4. 4.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 7 days
5. 5.If 2 pens cost ₹22, how much do 8 pens cost? (a) ₹28 (b) ₹176 (c) ₹88 (d) ₹99
6. 6.If 7 kites cost ₹49, how much do 8 kites cost? (a) ₹50 (b) ₹63 (c) ₹392 (d) ₹56
7. 7.₹115 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹93 (b) ₹115 (c) ₹92 (d) ₹23
8. 8.If 2 notebooks cost ₹30, how much do 10 notebooks cost? (a) ₹150 (b) ₹38 (c) ₹300 (d) ₹165
9. 9.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 17 days (c) 5 days (d) 6 days
10. 10.₹230 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹69 (b) ₹115 (c) ₹23 (d) ₹161
11. 11.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 20 days (c) 5 days (d) 15 days
12. 12.₹264 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹110 (b) ₹132 (c) ₹154 (d) ₹22
13. 13.If 4 pens cost ₹16, how much do 11 pens cost? (a) ₹48 (b) ₹23 (c) ₹176 (d) ₹44
14. 14.₹126 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹36 (b) ₹90 (c) ₹63 (d) ₹18
15. 15.If 3 pens cost ₹21, how much do 5 pens cost? (a) ₹42 (b) ₹105 (c) ₹23 (d) ₹35
16. 16.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 14 days (b) 18 days (c) 19 days (d) 6 days
17. 17.If 2 pens cost ₹50, how much do 8 pens cost? (a) ₹56 (b) ₹400 (c) ₹225 (d) ₹200
18. 18.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 11 days (d) 15 days
19. 19.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 3 days (d) 6 days
20. 20.If 4 notebooks cost ₹12, how much do 10 notebooks cost? (a) ₹120 (b) ₹30 (c) ₹18 (d) ₹33
21. 21.If 2 pens cost ₹10, how much do 3 pens cost? (a) ₹11 (b) ₹20 (c) ₹15 (d) ₹30
22. 22.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 25 days (b) 4 days (c) 5 days (d) 16 days
23. 23.If 2 kites cost ₹30, how much do 7 kites cost? (a) ₹35 (b) ₹105 (c) ₹120 (d) ₹210
24. 24.If 4 notebooks cost ₹52, how much do 9 notebooks cost? (a) ₹57 (b) ₹117 (c) ₹130 (d) ₹468
25. 25.₹104 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹8 (b) ₹52 (c) ₹40 (d) ₹64
26. 26.If 6 mangoes cost ₹96, how much do 4 mangoes cost? (a) ₹384 (b) ₹94 (c) ₹80 (d) ₹64
27. 27.If 7 pens cost ₹35, how much do 9 pens cost? (a) ₹45 (b) ₹315 (c) ₹37 (d) ₹50
28. 28.6 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 9 days (d) 25 days
29. 29.If 6 kites cost ₹30, how much do 2 kites cost? (a) ₹10 (b) ₹60 (c) ₹15 (d) ₹26
30. 30.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 4 days (d) 8 days
31. 31.If 6 notebooks cost ₹138, how much do 4 notebooks cost? (a) ₹92 (b) ₹115 (c) ₹136 (d) ₹552
32. 32.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 13 days (c) 15 days (d) 22 days
33. 33.₹377 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹261 (b) ₹232 (c) ₹29 (d) ₹145
34. 34.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 49 days (c) 9 days (d) 19 days
35. 35.8 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 7 days (d) 6 days
36. 36.₹130 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹78 (b) ₹65 (c) ₹26 (d) ₹52
37. 37.₹333 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹296 (b) ₹74 (c) ₹37 (d) ₹259
38. 38.If 3 pens cost ₹18, how much do 5 pens cost? (a) ₹30 (b) ₹20 (c) ₹90 (d) ₹36
39. 39.If 6 mangoes cost ₹72, how much do 9 mangoes cost? (a) ₹120 (b) ₹648 (c) ₹108 (d) ₹75
40. 40.If 7 kites cost ₹168, how much do 4 kites cost? (a) ₹96 (b) ₹672 (c) ₹165 (d) ₹120

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