Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 956 · 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.₹140 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹105 (b) ₹35 (c) ₹140 (d) ₹70
2. 2.₹85 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹69 (b) ₹85 (c) ₹17 (d) ₹68
3. 3.₹145 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹116 (b) ₹117 (c) ₹145 (d) ₹29
4. 4.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 18 days (c) 4 days (d) 3 days
5. 5.If 6 notebooks cost ₹126, how much do 4 notebooks cost? (a) ₹124 (b) ₹84 (c) ₹105 (d) ₹504
6. 6.If 7 mangoes cost ₹77, how much do 8 mangoes cost? (a) ₹99 (b) ₹88 (c) ₹78 (d) ₹616
7. 7.₹550 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹275 (b) ₹100 (c) ₹450 (d) ₹50
8. 8.₹63 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹14 (b) ₹7 (c) ₹56 (d) ₹49
9. 9.If 4 kites cost ₹44, how much do 5 kites cost? (a) ₹66 (b) ₹45 (c) ₹220 (d) ₹55
10. 10.If 8 pens cost ₹88, how much do 6 pens cost? (a) ₹77 (b) ₹86 (c) ₹528 (d) ₹66
11. 11.₹105 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹15 (b) ₹90 (c) ₹30 (d) ₹75
12. 12.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 1 day
13. 13.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 8 days (c) 56 days (d) 20 days
14. 14.If 4 notebooks cost ₹68, how much do 9 notebooks cost? (a) ₹73 (b) ₹612 (c) ₹170 (d) ₹153
15. 15.₹168 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹84 (b) ₹63 (c) ₹21 (d) ₹105
16. 16.If 7 mangoes cost ₹70, how much do 6 mangoes cost? (a) ₹420 (b) ₹69 (c) ₹60 (d) ₹70
17. 17.If 7 kites cost ₹49, how much do 6 kites cost? (a) ₹49 (b) ₹42 (c) ₹48 (d) ₹294
18. 18.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 27 days (d) 13 days
19. 19.If 6 mangoes cost ₹150, how much do 7 mangoes cost? (a) ₹151 (b) ₹200 (c) ₹175 (d) ₹1050
20. 20.8 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 20 days (b) 13 days (c) 17 days (d) 21 days
21. 21.If 4 notebooks cost ₹96, how much do 2 notebooks cost? (a) ₹192 (b) ₹94 (c) ₹48 (d) ₹72
22. 22.If 8 kites cost ₹56, how much do 5 kites cost? (a) ₹42 (b) ₹53 (c) ₹35 (d) ₹280
23. 23.₹363 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹231 (b) ₹264 (c) ₹33 (d) ₹132
24. 24.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 24 days (b) 14 days (c) 2 days (d) 25 days
25. 25.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 3 days
26. 26.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 7 days (d) 3 days
27. 27.If 4 notebooks cost ₹56, how much do 2 notebooks cost? (a) ₹112 (b) ₹42 (c) ₹54 (d) ₹28
28. 28.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 18 days (c) 9 days (d) 8 days
29. 29.If 7 pens cost ₹77, how much do 11 pens cost? (a) ₹81 (b) ₹847 (c) ₹132 (d) ₹121
30. 30.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 20 days (c) 14 days (d) 5 days
31. 31.If 2 mangoes cost ₹28, how much do 7 mangoes cost? (a) ₹98 (b) ₹196 (c) ₹33 (d) ₹112
32. 32.If 4 mangoes cost ₹28, how much do 9 mangoes cost? (a) ₹70 (b) ₹63 (c) ₹252 (d) ₹33
33. 33.₹611 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹470 (b) ₹188 (c) ₹423 (d) ₹47
34. 34.5 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 31 days (b) 15 days (c) 30 days (d) 9 days
35. 35.₹63 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹43 (b) ₹63 (c) ₹21 (d) ₹42
36. 36.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 4 days (d) 5 days
37. 37.If 4 mangoes cost ₹72, how much do 6 mangoes cost? (a) ₹126 (b) ₹74 (c) ₹108 (d) ₹432
38. 38.If 3 notebooks cost ₹9, how much do 4 notebooks cost? (a) ₹36 (b) ₹12 (c) ₹15 (d) ₹10
39. 39.₹200 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹60 (b) ₹100 (c) ₹20 (d) ₹140
40. 40.If 5 kites cost ₹25, how much do 11 kites cost? (a) ₹275 (b) ₹31 (c) ₹55 (d) ₹60

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