Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 837 · 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.If 3 pens cost ₹18, how much do 9 pens cost? (a) ₹24 (b) ₹162 (c) ₹60 (d) ₹54
2. 2.If 5 mangoes cost ₹55, how much do 6 mangoes cost? (a) ₹66 (b) ₹77 (c) ₹330 (d) ₹56
3. 3.₹376 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹188 (b) ₹235 (c) ₹47 (d) ₹141
4. 4.If 5 notebooks cost ₹45, how much do 12 notebooks cost? (a) ₹52 (b) ₹540 (c) ₹117 (d) ₹108
5. 5.If 8 pens cost ₹176, how much do 7 pens cost? (a) ₹175 (b) ₹176 (c) ₹1232 (d) ₹154
6. 6.If 3 kites cost ₹54, how much do 10 kites cost? (a) ₹180 (b) ₹198 (c) ₹540 (d) ₹61
7. 7.₹119 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹85 (b) ₹17 (c) ₹68 (d) ₹51
8. 8.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 33 days (c) 34 days (d) 7 days
9. 9.If 2 pens cost ₹10, how much do 4 pens cost? (a) ₹12 (b) ₹20 (c) ₹25 (d) ₹40
10. 10.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 36 days (c) 37 days (d) 15 days
11. 11.If 8 pens cost ₹48, how much do 2 pens cost? (a) ₹18 (b) ₹42 (c) ₹12 (d) ₹96
12. 12.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 11 days (d) 28 days
13. 13.If 2 kites cost ₹12, how much do 11 kites cost? (a) ₹66 (b) ₹21 (c) ₹72 (d) ₹132
14. 14.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 4 days (d) 3 days
15. 15.₹117 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹36 (b) ₹9 (c) ₹90 (d) ₹81
16. 16.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 7 days (c) 10 days (d) 6 days
17. 17.If 9 pens cost ₹162, how much do 10 pens cost? (a) ₹180 (b) ₹198 (c) ₹1620 (d) ₹163
18. 18.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 28 days (c) 27 days (d) 13 days
19. 19.If 8 notebooks cost ₹40, how much do 6 notebooks cost? (a) ₹38 (b) ₹30 (c) ₹35 (d) ₹240
20. 20.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 56 days (c) 8 days (d) 57 days
21. 21.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 2 days (c) 3 days (d) 4 days
22. 22.₹121 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹77 (b) ₹11 (c) ₹44 (d) ₹88
23. 23.If 2 notebooks cost ₹22, how much do 10 notebooks cost? (a) ₹220 (b) ₹110 (c) ₹121 (d) ₹30
24. 24.₹432 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹432 (b) ₹216 (c) ₹384 (d) ₹48
25. 25.₹517 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹329 (b) ₹235 (c) ₹282 (d) ₹47
26. 26.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 8 days (c) 4 days (d) 9 days
27. 27.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 21 days (d) 20 days
28. 28.₹319 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹145 (b) ₹29 (c) ₹203 (d) ₹174
29. 29.₹216 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹90 (b) ₹108 (c) ₹126 (d) ₹18
30. 30.If 5 notebooks cost ₹85, how much do 7 notebooks cost? (a) ₹119 (b) ₹87 (c) ₹136 (d) ₹595
31. 31.If 3 pens cost ₹18, how much do 6 pens cost? (a) ₹21 (b) ₹42 (c) ₹36 (d) ₹108
32. 32.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 3 days (d) 2 days
33. 33.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 19 days (c) 18 days (d) 10 days
34. 34.₹370 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹259 (b) ₹185 (c) ₹37 (d) ₹111
35. 35.₹322 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹23 (b) ₹115 (c) ₹207 (d) ₹161
36. 36.If 7 notebooks cost ₹98, how much do 11 notebooks cost? (a) ₹168 (b) ₹102 (c) ₹154 (d) ₹1078
37. 37.If 4 notebooks cost ₹60, how much do 5 notebooks cost? (a) ₹75 (b) ₹300 (c) ₹61 (d) ₹90
38. 38.₹120 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹15 (b) ₹120 (c) ₹105 (d) ₹60
39. 39.₹231 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹147 (b) ₹21 (c) ₹105 (d) ₹126
40. 40.₹416 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹208 (b) ₹32 (c) ₹256 (d) ₹160

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