Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 636 · 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.₹252 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹28 (b) ₹252 (c) ₹224 (d) ₹126
2. 2.If 8 pens cost ₹112, how much do 4 pens cost? (a) ₹70 (b) ₹56 (c) ₹108 (d) ₹448
3. 3.If 8 mangoes cost ₹152, how much do 6 mangoes cost? (a) ₹150 (b) ₹133 (c) ₹912 (d) ₹114
4. 4.₹132 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹60 (b) ₹66 (c) ₹12 (d) ₹72
5. 5.If 9 pens cost ₹153, how much do 10 pens cost? (a) ₹187 (b) ₹1530 (c) ₹170 (d) ₹154
6. 6.If 3 notebooks cost ₹33, how much do 12 notebooks cost? (a) ₹132 (b) ₹396 (c) ₹143 (d) ₹42
7. 7.If 4 mangoes cost ₹20, how much do 6 mangoes cost? (a) ₹22 (b) ₹120 (c) ₹30 (d) ₹35
8. 8.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 13 days (d) 28 days
9. 9.If 3 pens cost ₹42, how much do 8 pens cost? (a) ₹336 (b) ₹47 (c) ₹126 (d) ₹112
10. 10.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 6 days (d) 24 days
11. 11.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 16 days (d) 9 days
12. 12.₹88 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹44 (b) ₹77 (c) ₹88 (d) ₹11
13. 13.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 7 days (d) 28 days
14. 14.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 8 days (d) 12 days
15. 15.If 4 mangoes cost ₹28, how much do 7 mangoes cost? (a) ₹31 (b) ₹49 (c) ₹196 (d) ₹56
16. 16.If 5 pens cost ₹65, how much do 9 pens cost? (a) ₹585 (b) ₹130 (c) ₹117 (d) ₹69
17. 17.₹145 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹116 (b) ₹29 (c) ₹145 (d) ₹117
18. 18.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 17 days (b) 2 days (c) 3 days (d) 4 days
19. 19.₹32 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹16 (b) ₹32 (c) ₹8 (d) ₹24
20. 20.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 30 days (b) 31 days (c) 19 days (d) 11 days
21. 21.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 4 days (d) 2 days
22. 22.₹308 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹84 (b) ₹28 (c) ₹224 (d) ₹154
23. 23.₹396 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹108 (b) ₹288 (c) ₹198 (d) ₹36
24. 24.If 2 notebooks cost ₹40, how much do 9 notebooks cost? (a) ₹200 (b) ₹360 (c) ₹47 (d) ₹180
25. 25.If 4 kites cost ₹28, how much do 3 kites cost? (a) ₹84 (b) ₹21 (c) ₹28 (d) ₹27
26. 26.₹147 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹63 (b) ₹21 (c) ₹105 (d) ₹84
27. 27.If 3 notebooks cost ₹27, how much do 4 notebooks cost? (a) ₹36 (b) ₹45 (c) ₹28 (d) ₹108
28. 28.If 4 pens cost ₹84, how much do 6 pens cost? (a) ₹504 (b) ₹86 (c) ₹126 (d) ₹147
29. 29.If 5 pens cost ₹25, how much do 8 pens cost? (a) ₹45 (b) ₹40 (c) ₹200 (d) ₹28
30. 30.If 2 mangoes cost ₹18, how much do 7 mangoes cost? (a) ₹63 (b) ₹126 (c) ₹72 (d) ₹23
31. 31.If 2 mangoes cost ₹34, how much do 3 mangoes cost? (a) ₹51 (b) ₹35 (c) ₹68 (d) ₹102
32. 32.If 8 notebooks cost ₹168, how much do 5 notebooks cost? (a) ₹840 (b) ₹126 (c) ₹105 (d) ₹165
33. 33.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 6 days (c) 8 days (d) 9 days
34. 34.If 6 pens cost ₹108, how much do 5 pens cost? (a) ₹90 (b) ₹108 (c) ₹540 (d) ₹107
35. 35.₹110 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹33 (b) ₹77 (c) ₹11 (d) ₹55
36. 36.₹78 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹39 (b) ₹54 (c) ₹24 (d) ₹6
37. 37.₹133 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹19 (b) ₹133 (c) ₹115 (d) ₹114
38. 38.₹312 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹130 (b) ₹26 (c) ₹182 (d) ₹156
39. 39.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 15 days (d) 21 days
40. 40.If 5 notebooks cost ₹30, how much do 10 notebooks cost? (a) ₹300 (b) ₹66 (c) ₹35 (d) ₹60

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