Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 659 · 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 7 notebooks cost ₹119, how much do 11 notebooks cost? (a) ₹187 (b) ₹123 (c) ₹1309 (d) ₹204
2. 2.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 15 days (c) 13 days (d) 9 days
3. 3.₹574 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹205 (b) ₹369 (c) ₹287 (d) ₹41
4. 4.If 3 pens cost ₹36, how much do 4 pens cost? (a) ₹60 (b) ₹37 (c) ₹144 (d) ₹48
5. 5.₹18 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹6 (b) ₹9 (c) ₹18 (d) ₹12
6. 6.If 3 notebooks cost ₹24, how much do 5 notebooks cost? (a) ₹26 (b) ₹40 (c) ₹48 (d) ₹120
7. 7.₹319 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹29 (b) ₹290 (c) ₹261 (d) ₹58
8. 8.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 25 days (d) 17 days
9. 9.If 8 pens cost ₹40, how much do 12 pens cost? (a) ₹60 (b) ₹44 (c) ₹65 (d) ₹480
10. 10.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 8 days (d) 4 days
11. 11.If 3 pens cost ₹18, how much do 10 pens cost? (a) ₹25 (b) ₹180 (c) ₹60 (d) ₹66
12. 12.If 5 pens cost ₹25, how much do 12 pens cost? (a) ₹300 (b) ₹65 (c) ₹60 (d) ₹32
13. 13.₹297 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹27 (b) ₹135 (c) ₹189 (d) ₹162
14. 14.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 3 days (d) 5 days
15. 15.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 42 days (c) 43 days (d) 17 days
16. 16.If 2 pens cost ₹42, how much do 10 pens cost? (a) ₹420 (b) ₹50 (c) ₹231 (d) ₹210
17. 17.If 3 mangoes cost ₹33, how much do 5 mangoes cost? (a) ₹165 (b) ₹35 (c) ₹55 (d) ₹66
18. 18.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 6 days (d) 5 days
19. 19.₹189 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹126 (b) ₹21 (c) ₹84 (d) ₹105
20. 20.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 20 days (c) 5 days (d) 13 days
21. 21.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 8 days (d) 2 days
22. 22.₹336 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹120 (b) ₹216 (c) ₹168 (d) ₹24
23. 23.₹165 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹75 (b) ₹90 (c) ₹15 (d) ₹105
24. 24.If 8 kites cost ₹176, how much do 12 kites cost? (a) ₹286 (b) ₹2112 (c) ₹180 (d) ₹264
25. 25.6 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 14 days (b) 4 days (c) 2 days (d) 16 days
26. 26.₹69 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹46 (b) ₹23 (c) ₹47 (d) ₹69
27. 27.If 7 mangoes cost ₹28, how much do 5 mangoes cost? (a) ₹20 (b) ₹24 (c) ₹26 (d) ₹140
28. 28.If 5 mangoes cost ₹45, how much do 7 mangoes cost? (a) ₹72 (b) ₹63 (c) ₹315 (d) ₹47
29. 29.₹228 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹190 (b) ₹228 (c) ₹38 (d) ₹114
30. 30.If 2 pens cost ₹20, how much do 3 pens cost? (a) ₹30 (b) ₹40 (c) ₹60 (d) ₹21
31. 31.₹700 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹350 (b) ₹250 (c) ₹50 (d) ₹450
32. 32.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 27 days (c) 16 days (d) 26 days
33. 33.₹172 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹43 (b) ₹129 (c) ₹86 (d) ₹172
34. 34.₹324 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹252 (b) ₹72 (c) ₹36 (d) ₹162
35. 35.If 4 notebooks cost ₹88, how much do 2 notebooks cost? (a) ₹86 (b) ₹176 (c) ₹44 (d) ₹66
36. 36.₹378 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹135 (b) ₹243 (c) ₹189 (d) ₹27
37. 37.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 28 days (d) 27 days
38. 38.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 8 days (d) 14 days
39. 39.₹220 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹220 (b) ₹110 (c) ₹44 (d) ₹176
40. 40.If 5 pens cost ₹95, how much do 8 pens cost? (a) ₹98 (b) ₹171 (c) ₹760 (d) ₹152

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