Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 137 · 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 2 notebooks cost ₹40, how much do 12 notebooks cost? (a) ₹240 (b) ₹260 (c) ₹480 (d) ₹50
2. 2.If 6 mangoes cost ₹126, how much do 8 mangoes cost? (a) ₹189 (b) ₹168 (c) ₹128 (d) ₹1008
3. 3.If 6 pens cost ₹132, how much do 11 pens cost? (a) ₹137 (b) ₹1452 (c) ₹242 (d) ₹264
4. 4.₹270 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹30 (b) ₹135 (c) ₹60 (d) ₹210
5. 5.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 6 days (d) 4 days
6. 6.If 8 pens cost ₹136, how much do 3 pens cost? (a) ₹68 (b) ₹131 (c) ₹408 (d) ₹51
7. 7.If 7 mangoes cost ₹63, how much do 2 mangoes cost? (a) ₹126 (b) ₹18 (c) ₹58 (d) ₹27
8. 8.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 36 days (c) 15 days (d) 35 days
9. 9.If 3 kites cost ₹72, how much do 10 kites cost? (a) ₹720 (b) ₹79 (c) ₹240 (d) ₹264
10. 10.If 7 notebooks cost ₹49, how much do 5 notebooks cost? (a) ₹47 (b) ₹42 (c) ₹35 (d) ₹245
11. 11.₹352 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹176 (b) ₹308 (c) ₹352 (d) ₹44
12. 12.If 4 mangoes cost ₹20, how much do 5 mangoes cost? (a) ₹25 (b) ₹100 (c) ₹21 (d) ₹30
13. 13.If 2 kites cost ₹8, how much do 3 kites cost? (a) ₹24 (b) ₹12 (c) ₹9 (d) ₹16
14. 14.₹341 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹62 (b) ₹31 (c) ₹279 (d) ₹310
15. 15.₹182 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹14 (b) ₹112 (c) ₹70 (d) ₹91
16. 16.₹70 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹7 (b) ₹70 (c) ₹35 (d) ₹63
17. 17.₹296 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹296 (b) ₹148 (c) ₹259 (d) ₹37
18. 18.If 4 pens cost ₹60, how much do 5 pens cost? (a) ₹61 (b) ₹75 (c) ₹300 (d) ₹90
19. 19.If 6 mangoes cost ₹102, how much do 7 mangoes cost? (a) ₹119 (b) ₹103 (c) ₹714 (d) ₹136
20. 20.If 7 notebooks cost ₹77, how much do 4 notebooks cost? (a) ₹44 (b) ₹74 (c) ₹308 (d) ₹55
21. 21.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 13 days (c) 7 days (d) 6 days
22. 22.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 26 days (d) 27 days
23. 23.If 7 notebooks cost ₹133, how much do 11 notebooks cost? (a) ₹228 (b) ₹209 (c) ₹137 (d) ₹1463
24. 24.₹418 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹209 (b) ₹38 (c) ₹228 (d) ₹190
25. 25.If 8 pens cost ₹56, how much do 11 pens cost? (a) ₹77 (b) ₹84 (c) ₹59 (d) ₹616
26. 26.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 10 days (d) 12 days
27. 27.If 7 notebooks cost ₹21, how much do 3 notebooks cost? (a) ₹63 (b) ₹17 (c) ₹9 (d) ₹12
28. 28.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 12 days (d) 11 days
29. 29.7 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) 21 days (d) 22 days
30. 30.If 2 mangoes cost ₹40, how much do 7 mangoes cost? (a) ₹45 (b) ₹140 (c) ₹280 (d) ₹160
31. 31.If 7 notebooks cost ₹98, how much do 8 notebooks cost? (a) ₹784 (b) ₹112 (c) ₹126 (d) ₹99
32. 32.₹180 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹180 (b) ₹30 (c) ₹90 (d) ₹150
33. 33.If 4 notebooks cost ₹92, how much do 6 notebooks cost? (a) ₹138 (b) ₹552 (c) ₹94 (d) ₹161
34. 34.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 27 days (d) 28 days
35. 35.If 4 notebooks cost ₹72, how much do 8 notebooks cost? (a) ₹576 (b) ₹76 (c) ₹162 (d) ₹144
36. 36.If 8 notebooks cost ₹40, how much do 9 notebooks cost? (a) ₹50 (b) ₹41 (c) ₹360 (d) ₹45
37. 37.₹280 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹140 (b) ₹280 (c) ₹240 (d) ₹40
38. 38.If 9 mangoes cost ₹90, how much do 12 mangoes cost? (a) ₹130 (b) ₹120 (c) ₹93 (d) ₹1080
39. 39.₹114 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹38 (b) ₹57 (c) ₹114 (d) ₹76
40. 40.If 6 kites cost ₹108, how much do 3 kites cost? (a) ₹324 (b) ₹72 (c) ₹54 (d) ₹105

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