Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 408 · 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. 1.9 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 12 days (c) 5 days (d) 11 days
2. 2.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 27 days (d) 15 days
3. 3.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 12 days
4. 4.If 4 pens cost ₹88, how much do 12 pens cost? (a) ₹286 (b) ₹264 (c) ₹96 (d) ₹1056
5. 5.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 13 days (c) 21 days (d) 22 days
6. 6.₹517 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹329 (b) ₹282 (c) ₹47 (d) ₹235
7. 7.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 4 days (d) 10 days
8. 8.7 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
9. 9.₹105 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹30 (b) ₹15 (c) ₹90 (d) ₹75
10. 10.₹77 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹33 (b) ₹55 (c) ₹11 (d) ₹44
11. 11.₹132 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹36 (b) ₹96 (c) ₹12 (d) ₹66
12. 12.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 14 days (b) 6 days (c) 20 days (d) 5 days
13. 13.If 3 notebooks cost ₹75, how much do 9 notebooks cost? (a) ₹81 (b) ₹250 (c) ₹225 (d) ₹675
14. 14.If 9 mangoes cost ₹36, how much do 10 mangoes cost? (a) ₹37 (b) ₹360 (c) ₹44 (d) ₹40
15. 15.₹144 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹72 (b) ₹80 (c) ₹16 (d) ₹64
16. 16.If 6 pens cost ₹54, how much do 12 pens cost? (a) ₹108 (b) ₹117 (c) ₹60 (d) ₹648
17. 17.If 9 mangoes cost ₹144, how much do 8 mangoes cost? (a) ₹144 (b) ₹1152 (c) ₹128 (d) ₹143
18. 18.₹342 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹152 (b) ₹190 (c) ₹38 (d) ₹171
19. 19.If 3 notebooks cost ₹51, how much do 12 notebooks cost? (a) ₹204 (b) ₹612 (c) ₹60 (d) ₹221
20. 20.₹315 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹90 (b) ₹225 (c) ₹270 (d) ₹45
21. 21.If 3 mangoes cost ₹18, how much do 4 mangoes cost? (a) ₹19 (b) ₹30 (c) ₹72 (d) ₹24
22. 22.If 8 kites cost ₹136, how much do 4 kites cost? (a) ₹85 (b) ₹132 (c) ₹544 (d) ₹68
23. 23.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 10 days (d) 7 days
24. 24.If 4 notebooks cost ₹12, how much do 3 notebooks cost? (a) ₹9 (b) ₹11 (c) ₹12 (d) ₹36
25. 25.₹416 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹288 (b) ₹208 (c) ₹128 (d) ₹32
26. 26.If 5 kites cost ₹75, how much do 4 kites cost? (a) ₹300 (b) ₹75 (c) ₹60 (d) ₹74
27. 27.If 5 notebooks cost ₹85, how much do 7 notebooks cost? (a) ₹119 (b) ₹595 (c) ₹136 (d) ₹87
28. 28.₹84 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹35 (b) ₹42 (c) ₹49 (d) ₹7
29. 29.If 4 kites cost ₹12, how much do 2 kites cost? (a) ₹6 (b) ₹10 (c) ₹9 (d) ₹24
30. 30.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 19 days (d) 2 days
31. 31.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹8 (b) ₹40 (c) ₹44 (d) ₹48
32. 32.₹189 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹21 (b) ₹84 (c) ₹126 (d) ₹105
33. 33.If 4 mangoes cost ₹40, how much do 2 mangoes cost? (a) ₹80 (b) ₹30 (c) ₹20 (d) ₹38
34. 34.If 3 mangoes cost ₹39, how much do 10 mangoes cost? (a) ₹46 (b) ₹130 (c) ₹143 (d) ₹390
35. 35.₹259 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹37 (b) ₹111 (c) ₹185 (d) ₹148
36. 36.₹273 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹168 (b) ₹21 (c) ₹105 (d) ₹189
37. 37.If 5 kites cost ₹65, how much do 6 kites cost? (a) ₹91 (b) ₹66 (c) ₹78 (d) ₹390
38. 38.If 7 pens cost ₹49, how much do 5 pens cost? (a) ₹35 (b) ₹245 (c) ₹42 (d) ₹47
39. 39.₹147 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹42 (b) ₹105 (c) ₹126 (d) ₹21
40. 40.If 4 pens cost ₹28, how much do 3 pens cost? (a) ₹28 (b) ₹27 (c) ₹84 (d) ₹21

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