Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 660 · 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.₹572 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹176 (b) ₹44 (c) ₹396 (d) ₹286
2. 2.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 8 days (d) 7 days
3. 3.If 9 pens cost ₹45, how much do 11 pens cost? (a) ₹47 (b) ₹495 (c) ₹55 (d) ₹60
4. 4.₹390 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹195 (b) ₹30 (c) ₹240 (d) ₹150
5. 5.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 21 days (b) 11 days (c) 17 days (d) 22 days
6. 6.₹264 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹24 (b) ₹120 (c) ₹132 (d) ₹144
7. 7.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 10 days (d) 8 days
8. 8.8 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 9 days (d) 7 days
9. 9.₹210 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹175 (b) ₹35 (c) ₹210 (d) ₹105
10. 10.₹240 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹120 (b) ₹20 (c) ₹100 (d) ₹140
11. 11.If 3 notebooks cost ₹57, how much do 5 notebooks cost? (a) ₹285 (b) ₹59 (c) ₹95 (d) ₹114
12. 12.If 8 notebooks cost ₹136, how much do 6 notebooks cost? (a) ₹816 (b) ₹134 (c) ₹102 (d) ₹119
13. 13.₹153 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹17 (b) ₹68 (c) ₹85 (d) ₹102
14. 14.If 6 notebooks cost ₹54, how much do 9 notebooks cost? (a) ₹81 (b) ₹486 (c) ₹57 (d) ₹90
15. 15.8 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 20 days (c) 41 days (d) 40 days
16. 16.If 2 notebooks cost ₹28, how much do 7 notebooks cost? (a) ₹33 (b) ₹196 (c) ₹112 (d) ₹98
17. 17.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 7 days (d) 2 days
18. 18.₹156 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹65 (b) ₹13 (c) ₹78 (d) ₹91
19. 19.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 22 days (d) 21 days
20. 20.₹91 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹39 (b) ₹13 (c) ₹65 (d) ₹52
21. 21.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 12 days (c) 2 days (d) 18 days
22. 22.If 2 kites cost ₹32, how much do 6 kites cost? (a) ₹112 (b) ₹192 (c) ₹96 (d) ₹36
23. 23.₹528 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹432 (b) ₹48 (c) ₹96 (d) ₹264
24. 24.If 5 notebooks cost ₹60, how much do 4 notebooks cost? (a) ₹240 (b) ₹60 (c) ₹59 (d) ₹48
25. 25.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 19 days
26. 26.If 3 mangoes cost ₹51, how much do 8 mangoes cost? (a) ₹153 (b) ₹56 (c) ₹408 (d) ₹136
27. 27.If 2 kites cost ₹44, how much do 11 kites cost? (a) ₹484 (b) ₹53 (c) ₹242 (d) ₹264
28. 28.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 19 days (c) 14 days (d) 18 days
29. 29.₹154 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹84 (b) ₹77 (c) ₹70 (d) ₹14
30. 30.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 24 days (c) 25 days (d) 12 days
31. 31.₹341 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹279 (b) ₹31 (c) ₹93 (d) ₹248
32. 32.If 2 pens cost ₹46, how much do 8 pens cost? (a) ₹184 (b) ₹207 (c) ₹368 (d) ₹52
33. 33.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 1 day (b) 3 days (c) 8 days (d) 2 days
34. 34.₹430 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹215 (b) ₹430 (c) ₹43 (d) ₹387
35. 35.If 5 kites cost ₹125, how much do 12 kites cost? (a) ₹1500 (b) ₹300 (c) ₹325 (d) ₹132
36. 36.If 3 kites cost ₹9, how much do 7 kites cost? (a) ₹24 (b) ₹13 (c) ₹21 (d) ₹63
37. 37.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 3 days (d) 2 days
38. 38.If 7 kites cost ₹70, how much do 3 kites cost? (a) ₹66 (b) ₹40 (c) ₹210 (d) ₹30
39. 39.If 4 notebooks cost ₹76, how much do 2 notebooks cost? (a) ₹74 (b) ₹38 (c) ₹57 (d) ₹152
40. 40.If 7 pens cost ₹175, how much do 2 pens cost? (a) ₹170 (b) ₹350 (c) ₹50 (d) ₹75

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