Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 298 · 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 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 21 days (c) 13 days (d) 22 days
2. 2.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 28 days (c) 15 days (d) 3 days
3. 3.₹104 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹39 (b) ₹52 (c) ₹65 (d) ₹13
4. 4.₹310 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹310 (b) ₹279 (c) ₹155 (d) ₹31
5. 5.₹440 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹40 (b) ₹220 (c) ₹360 (d) ₹80
6. 6.₹352 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹132 (b) ₹220 (c) ₹176 (d) ₹44
7. 7.If 4 pens cost ₹100, how much do 5 pens cost? (a) ₹500 (b) ₹150 (c) ₹101 (d) ₹125
8. 8.₹405 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹45 (b) ₹405 (c) ₹361 (d) ₹360
9. 9.9 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) 9 days (d) 8 days
10. 10.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 15 days
11. 11.If 7 kites cost ₹56, how much do 12 kites cost? (a) ₹96 (b) ₹61 (c) ₹672 (d) ₹104
12. 12.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 15 days (d) 14 days
13. 13.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 15 days (d) 2 days
14. 14.If 4 pens cost ₹76, how much do 3 pens cost? (a) ₹57 (b) ₹76 (c) ₹228 (d) ₹75
15. 15.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 1 day (c) 11 days (d) 21 days
16. 16.If 7 mangoes cost ₹147, how much do 2 mangoes cost? (a) ₹142 (b) ₹63 (c) ₹42 (d) ₹294
17. 17.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 4 days (d) 5 days
18. 18.₹91 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹39 (b) ₹52 (c) ₹65 (d) ₹13
19. 19.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹44 (b) ₹66 (c) ₹11 (d) ₹55
20. 20.If 5 kites cost ₹15, how much do 4 kites cost? (a) ₹14 (b) ₹60 (c) ₹15 (d) ₹12
21. 21.If 3 mangoes cost ₹30, how much do 7 mangoes cost? (a) ₹210 (b) ₹80 (c) ₹34 (d) ₹70
22. 22.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 3 days (c) 11 days (d) 2 days
23. 23.₹120 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹48 (b) ₹60 (c) ₹72 (d) ₹24
24. 24.If 2 pens cost ₹8, how much do 9 pens cost? (a) ₹40 (b) ₹15 (c) ₹36 (d) ₹72
25. 25.If 5 kites cost ₹105, how much do 6 kites cost? (a) ₹630 (b) ₹126 (c) ₹147 (d) ₹106
26. 26.4 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 36 days (b) 20 days (c) 4 days (d) 5 days
27. 27.₹624 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹48 (b) ₹384 (c) ₹240 (d) ₹312
28. 28.₹84 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹84 (b) ₹42 (c) ₹70 (d) ₹14
29. 29.₹598 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹230 (b) ₹299 (c) ₹368 (d) ₹46
30. 30.If 5 mangoes cost ₹45, how much do 9 mangoes cost? (a) ₹49 (b) ₹405 (c) ₹90 (d) ₹81
31. 31.If 2 notebooks cost ₹14, how much do 3 notebooks cost? (a) ₹42 (b) ₹15 (c) ₹21 (d) ₹28
32. 32.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 39 days (c) 17 days (d) 40 days
33. 33.If 7 notebooks cost ₹63, how much do 6 notebooks cost? (a) ₹63 (b) ₹378 (c) ₹54 (d) ₹62
34. 34.If 4 pens cost ₹12, how much do 8 pens cost? (a) ₹24 (b) ₹27 (c) ₹16 (d) ₹96
35. 35.₹66 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹24 (b) ₹33 (c) ₹6 (d) ₹42
36. 36.₹319 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹58 (b) ₹261 (c) ₹290 (d) ₹29
37. 37.₹54 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹6 (b) ₹24 (c) ₹30 (d) ₹27
38. 38.If 4 kites cost ₹92, how much do 11 kites cost? (a) ₹1012 (b) ₹253 (c) ₹99 (d) ₹276
39. 39.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 12 days (c) 9 days (d) 4 days
40. 40.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 14 days (c) 8 days (d) 15 days

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