Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 603 · 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.₹170 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹85 (b) ₹68 (c) ₹102 (d) ₹34
2. 2.If 4 notebooks cost ₹84, how much do 11 notebooks cost? (a) ₹924 (b) ₹252 (c) ₹91 (d) ₹231
3. 3.₹396 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹44 (b) ₹198 (c) ₹308 (d) ₹88
4. 4.If 5 pens cost ₹25, how much do 3 pens cost? (a) ₹15 (b) ₹75 (c) ₹20 (d) ₹23
5. 5.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 7 days (d) 9 days
6. 6.If 7 pens cost ₹21, how much do 2 pens cost? (a) ₹16 (b) ₹6 (c) ₹9 (d) ₹42
7. 7.₹434 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹279 (b) ₹155 (c) ₹217 (d) ₹31
8. 8.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 10 days (d) 2 days
9. 9.If 3 notebooks cost ₹12, how much do 4 notebooks cost? (a) ₹16 (b) ₹48 (c) ₹20 (d) ₹13
10. 10.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 36 days (c) 15 days (d) 37 days
11. 11.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 13 days (c) 11 days (d) 12 days
12. 12.If 2 notebooks cost ₹22, how much do 11 notebooks cost? (a) ₹31 (b) ₹121 (c) ₹132 (d) ₹242
13. 13.If 2 notebooks cost ₹22, how much do 9 notebooks cost? (a) ₹198 (b) ₹29 (c) ₹99 (d) ₹110
14. 14.If 2 notebooks cost ₹20, how much do 3 notebooks cost? (a) ₹21 (b) ₹60 (c) ₹30 (d) ₹40
15. 15.₹117 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹79 (b) ₹39 (c) ₹117 (d) ₹78
16. 16.If 2 mangoes cost ₹36, how much do 3 mangoes cost? (a) ₹54 (b) ₹72 (c) ₹37 (d) ₹108
17. 17.₹49 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹43 (b) ₹42 (c) ₹49 (d) ₹7
18. 18.If 3 mangoes cost ₹12, how much do 4 mangoes cost? (a) ₹16 (b) ₹48 (c) ₹20 (d) ₹13
19. 19.If 4 notebooks cost ₹28, how much do 3 notebooks cost? (a) ₹27 (b) ₹21 (c) ₹84 (d) ₹28
20. 20.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 4 days (d) 2 days
21. 21.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 3 days (c) 48 days (d) 6 days
22. 22.If 6 notebooks cost ₹18, how much do 4 notebooks cost? (a) ₹72 (b) ₹16 (c) ₹15 (d) ₹12
23. 23.If 2 kites cost ₹36, how much do 4 kites cost? (a) ₹144 (b) ₹38 (c) ₹72 (d) ₹90
24. 24.₹517 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹423 (b) ₹376 (c) ₹47 (d) ₹141
25. 25.If 4 pens cost ₹48, how much do 8 pens cost? (a) ₹108 (b) ₹52 (c) ₹96 (d) ₹384
26. 26.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 19 days (d) 2 days
27. 27.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 11 days
28. 28.₹126 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹14 (b) ₹63 (c) ₹126 (d) ₹112
29. 29.If 4 pens cost ₹88, how much do 9 pens cost? (a) ₹198 (b) ₹792 (c) ₹93 (d) ₹220
30. 30.If 9 notebooks cost ₹171, how much do 8 notebooks cost? (a) ₹1368 (b) ₹171 (c) ₹152 (d) ₹170
31. 31.If 6 mangoes cost ₹24, how much do 5 mangoes cost? (a) ₹24 (b) ₹120 (c) ₹23 (d) ₹20
32. 32.₹140 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹80 (b) ₹70 (c) ₹20 (d) ₹60
33. 33.₹360 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹30 (b) ₹180 (c) ₹150 (d) ₹210
34. 34.If 5 notebooks cost ₹45, how much do 6 notebooks cost? (a) ₹54 (b) ₹63 (c) ₹270 (d) ₹46
35. 35.5 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
36. 36.If 5 pens cost ₹30, how much do 9 pens cost? (a) ₹54 (b) ₹60 (c) ₹34 (d) ₹270
37. 37.₹658 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹235 (b) ₹329 (c) ₹423 (d) ₹47
38. 38.If 6 notebooks cost ₹60, how much do 7 notebooks cost? (a) ₹420 (b) ₹70 (c) ₹61 (d) ₹80
39. 39.If 5 mangoes cost ₹25, how much do 12 mangoes cost? (a) ₹60 (b) ₹300 (c) ₹65 (d) ₹32
40. 40.₹209 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹152 (b) ₹57 (c) ₹19 (d) ₹171

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