Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 597 · 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.₹60 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹30 (b) ₹60 (c) ₹40 (d) ₹20
2. 2.₹611 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹423 (b) ₹188 (c) ₹47 (d) ₹470
3. 3.₹18 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹9 (b) ₹18 (c) ₹12 (d) ₹6
4. 4.If 8 kites cost ₹176, how much do 7 kites cost? (a) ₹1232 (b) ₹154 (c) ₹175 (d) ₹176
5. 5.₹546 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹42 (b) ₹336 (c) ₹210 (d) ₹273
6. 6.If 8 mangoes cost ₹104, how much do 11 mangoes cost? (a) ₹107 (b) ₹156 (c) ₹1144 (d) ₹143
7. 7.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 26 days (b) 17 days (c) 9 days (d) 27 days
8. 8.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 5 days (c) 45 days (d) 44 days
9. 9.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 11 days (d) 5 days
10. 10.₹136 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹136 (b) ₹68 (c) ₹34 (d) ₹102
11. 11.If 3 notebooks cost ₹15, how much do 12 notebooks cost? (a) ₹60 (b) ₹24 (c) ₹180 (d) ₹65
12. 12.If 8 pens cost ₹104, how much do 2 pens cost? (a) ₹98 (b) ₹208 (c) ₹26 (d) ₹39
13. 13.If 3 notebooks cost ₹72, how much do 6 notebooks cost? (a) ₹144 (b) ₹432 (c) ₹75 (d) ₹168
14. 14.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 7 days (d) 2 days
15. 15.If 5 mangoes cost ₹60, how much do 6 mangoes cost? (a) ₹61 (b) ₹84 (c) ₹360 (d) ₹72
16. 16.₹385 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹175 (b) ₹245 (c) ₹35 (d) ₹210
17. 17.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 18 days (c) 12 days (d) 19 days
18. 18.If 2 kites cost ₹24, how much do 11 kites cost? (a) ₹264 (b) ₹144 (c) ₹33 (d) ₹132
19. 19.6 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 16 days (b) 19 days (c) 18 days (d) 14 days
20. 20.₹99 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹81 (b) ₹72 (c) ₹27 (d) ₹9
21. 21.₹88 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹8 (b) ₹56 (c) ₹44 (d) ₹32
22. 22.₹72 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹42 (b) ₹30 (c) ₹36 (d) ₹6
23. 23.If 8 notebooks cost ₹56, how much do 11 notebooks cost? (a) ₹77 (b) ₹84 (c) ₹616 (d) ₹59
24. 24.₹54 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹6 (b) ₹27 (c) ₹48 (d) ₹54
25. 25.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 2 days (d) 3 days
26. 26.If 5 pens cost ₹90, how much do 6 pens cost? (a) ₹126 (b) ₹108 (c) ₹91 (d) ₹540
27. 27.If 6 mangoes cost ₹90, how much do 2 mangoes cost? (a) ₹180 (b) ₹45 (c) ₹86 (d) ₹30
28. 28.If 2 mangoes cost ₹48, how much do 9 mangoes cost? (a) ₹432 (b) ₹240 (c) ₹216 (d) ₹55
29. 29.₹56 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹35 (b) ₹21 (c) ₹28 (d) ₹7
30. 30.If 8 kites cost ₹136, how much do 2 kites cost? (a) ₹130 (b) ₹272 (c) ₹34 (d) ₹51
31. 31.₹90 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹9 (b) ₹45 (c) ₹90 (d) ₹81
32. 32.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 12 days (c) 10 days (d) 11 days
33. 33.₹441 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹49 (b) ₹245 (c) ₹294 (d) ₹196
34. 34.₹169 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹117 (b) ₹65 (c) ₹104 (d) ₹13
35. 35.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 32 days (c) 3 days (d) 17 days
36. 36.₹200 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹100 (b) ₹80 (c) ₹40 (d) ₹120
37. 37.₹330 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹165 (b) ₹231 (c) ₹99 (d) ₹33
38. 38.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 25 days (d) 9 days
39. 39.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 13 days (c) 15 days (d) 21 days
40. 40.If 6 kites cost ₹36, how much do 8 kites cost? (a) ₹288 (b) ₹38 (c) ₹54 (d) ₹48

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