Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 783 · 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 8 mangoes cost ₹184, how much do 2 mangoes cost? (a) ₹368 (b) ₹69 (c) ₹178 (d) ₹46
2. 2.If 3 pens cost ₹57, how much do 12 pens cost? (a) ₹228 (b) ₹684 (c) ₹247 (d) ₹66
3. 3.₹70 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹14 (b) ₹56 (c) ₹35 (d) ₹70
4. 4.₹500 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹250 (b) ₹500 (c) ₹50 (d) ₹450
5. 5.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 25 days (b) 17 days (c) 13 days (d) 9 days
6. 6.₹495 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹315 (b) ₹45 (c) ₹180 (d) ₹360
7. 7.₹296 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹296 (b) ₹259 (c) ₹148 (d) ₹37
8. 8.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 1 day (c) 15 days (d) 9 days
9. 9.If 9 kites cost ₹54, how much do 4 kites cost? (a) ₹30 (b) ₹216 (c) ₹49 (d) ₹24
10. 10.If 2 pens cost ₹40, how much do 10 pens cost? (a) ₹400 (b) ₹220 (c) ₹200 (d) ₹48
11. 11.If 2 notebooks cost ₹50, how much do 12 notebooks cost? (a) ₹325 (b) ₹60 (c) ₹300 (d) ₹600
12. 12.If 2 pens cost ₹10, how much do 8 pens cost? (a) ₹80 (b) ₹45 (c) ₹16 (d) ₹40
13. 13.If 2 pens cost ₹48, how much do 3 pens cost? (a) ₹72 (b) ₹96 (c) ₹49 (d) ₹144
14. 14.₹369 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹287 (b) ₹41 (c) ₹328 (d) ₹82
15. 15.₹198 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹99 (b) ₹162 (c) ₹36 (d) ₹18
16. 16.If 9 kites cost ₹27, how much do 10 kites cost? (a) ₹33 (b) ₹28 (c) ₹30 (d) ₹270
17. 17.If 2 notebooks cost ₹42, how much do 8 notebooks cost? (a) ₹168 (b) ₹48 (c) ₹336 (d) ₹189
18. 18.8 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 2 days (d) 9 days
19. 19.If 2 notebooks cost ₹38, how much do 4 notebooks cost? (a) ₹40 (b) ₹152 (c) ₹95 (d) ₹76
20. 20.If 6 mangoes cost ₹84, how much do 7 mangoes cost? (a) ₹85 (b) ₹112 (c) ₹588 (d) ₹98
21. 21.If 3 notebooks cost ₹21, how much do 7 notebooks cost? (a) ₹49 (b) ₹25 (c) ₹147 (d) ₹56
22. 22.If 4 kites cost ₹12, how much do 10 kites cost? (a) ₹18 (b) ₹33 (c) ₹120 (d) ₹30
23. 23.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 33 days (b) 5 days (c) 34 days (d) 17 days
24. 24.If 2 pens cost ₹24, how much do 4 pens cost? (a) ₹60 (b) ₹96 (c) ₹26 (d) ₹48
25. 25.If 5 mangoes cost ₹90, how much do 6 mangoes cost? (a) ₹108 (b) ₹540 (c) ₹91 (d) ₹126
26. 26.If 2 mangoes cost ₹6, how much do 10 mangoes cost? (a) ₹60 (b) ₹14 (c) ₹33 (d) ₹30
27. 27.If 2 notebooks cost ₹46, how much do 3 notebooks cost? (a) ₹69 (b) ₹138 (c) ₹47 (d) ₹92
28. 28.₹63 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹43 (b) ₹42 (c) ₹63 (d) ₹21
29. 29.₹80 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹80 (b) ₹40 (c) ₹64 (d) ₹16
30. 30.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 13 days (c) 5 days (d) 22 days
31. 31.If 8 kites cost ₹104, how much do 10 kites cost? (a) ₹143 (b) ₹1040 (c) ₹130 (d) ₹106
32. 32.If 8 pens cost ₹32, how much do 7 pens cost? (a) ₹31 (b) ₹224 (c) ₹32 (d) ₹28
33. 33.If 5 pens cost ₹40, how much do 6 pens cost? (a) ₹56 (b) ₹48 (c) ₹240 (d) ₹41
34. 34.If 6 kites cost ₹114, how much do 7 kites cost? (a) ₹798 (b) ₹133 (c) ₹152 (d) ₹115
35. 35.If 9 kites cost ₹126, how much do 5 kites cost? (a) ₹70 (b) ₹84 (c) ₹630 (d) ₹122
36. 36.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 48 days (b) 3 days (c) 6 days (d) 18 days
37. 37.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 1 day
38. 38.₹624 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹48 (b) ₹384 (c) ₹312 (d) ₹240
39. 39.₹138 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹92 (b) ₹138 (c) ₹46 (d) ₹69
40. 40.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 28 days (d) 27 days

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