Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 225 · 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.₹126 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹14 (b) ₹70 (c) ₹56 (d) ₹63
2. 2.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 12 days (d) 5 days
3. 3.₹423 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹376 (b) ₹94 (c) ₹47 (d) ₹329
4. 4.If 8 pens cost ₹56, how much do 2 pens cost? (a) ₹14 (b) ₹21 (c) ₹50 (d) ₹112
5. 5.₹264 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹48 (b) ₹24 (c) ₹216 (d) ₹132
6. 6.₹495 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹360 (b) ₹315 (c) ₹45 (d) ₹180
7. 7.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 1 day (d) 10 days
8. 8.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 27 days (b) 28 days (c) 17 days (d) 7 days
9. 9.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 15 days (d) 14 days
10. 10.₹200 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹200 (b) ₹20 (c) ₹100 (d) ₹180
11. 11.₹120 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹60 (b) ₹12 (c) ₹36 (d) ₹84
12. 12.If 7 kites cost ₹175, how much do 9 kites cost? (a) ₹1575 (b) ₹177 (c) ₹250 (d) ₹225
13. 13.If 8 mangoes cost ₹96, how much do 12 mangoes cost? (a) ₹1152 (b) ₹156 (c) ₹100 (d) ₹144
14. 14.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 13 days (b) 16 days (c) 4 days (d) 3 days
15. 15.4 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
16. 16.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 4 days (d) 9 days
17. 17.If 2 notebooks cost ₹16, how much do 3 notebooks cost? (a) ₹17 (b) ₹32 (c) ₹48 (d) ₹24
18. 18.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 31 days (d) 30 days
19. 19.If 6 mangoes cost ₹78, how much do 5 mangoes cost? (a) ₹390 (b) ₹65 (c) ₹77 (d) ₹78
20. 20.If 6 pens cost ₹42, how much do 11 pens cost? (a) ₹77 (b) ₹84 (c) ₹47 (d) ₹462
21. 21.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 36 days (b) 35 days (c) 11 days (d) 19 days
22. 22.If 5 pens cost ₹125, how much do 12 pens cost? (a) ₹132 (b) ₹325 (c) ₹1500 (d) ₹300
23. 23.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 13 days (d) 8 days
24. 24.If 3 notebooks cost ₹42, how much do 7 notebooks cost? (a) ₹294 (b) ₹112 (c) ₹46 (d) ₹98
25. 25.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 7 days (c) 15 days (d) 11 days
26. 26.If 3 pens cost ₹27, how much do 11 pens cost? (a) ₹108 (b) ₹99 (c) ₹35 (d) ₹297
27. 27.3 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) 22 days (d) 15 days
28. 28.₹273 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹210 (b) ₹21 (c) ₹189 (d) ₹84
29. 29.₹99 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹9 (b) ₹63 (c) ₹54 (d) ₹45
30. 30.If 9 notebooks cost ₹81, how much do 11 notebooks cost? (a) ₹83 (b) ₹108 (c) ₹99 (d) ₹891
31. 31.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 7 days (d) 6 days
32. 32.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 15 days (c) 27 days (d) 3 days
33. 33.If 3 notebooks cost ₹27, how much do 5 notebooks cost? (a) ₹29 (b) ₹54 (c) ₹135 (d) ₹45
34. 34.₹170 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹102 (b) ₹34 (c) ₹85 (d) ₹68
35. 35.If 8 pens cost ₹184, how much do 2 pens cost? (a) ₹368 (b) ₹178 (c) ₹46 (d) ₹69
36. 36.₹378 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹210 (b) ₹42 (c) ₹168 (d) ₹189
37. 37.₹117 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹13 (b) ₹65 (c) ₹78 (d) ₹52
38. 38.₹78 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹6 (b) ₹30 (c) ₹39 (d) ₹48
39. 39.₹423 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹235 (b) ₹188 (c) ₹47 (d) ₹282
40. 40.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 6 days (d) 7 days

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