Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 573 · 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. 1.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 13 days (c) 21 days (d) 1 day
2. 2.₹70 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹10 (b) ₹60 (c) ₹35 (d) ₹70
3. 3.If 5 notebooks cost ₹40, how much do 4 notebooks cost? (a) ₹39 (b) ₹160 (c) ₹40 (d) ₹32
4. 4.₹224 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹16 (b) ₹144 (c) ₹80 (d) ₹112
5. 5.₹184 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹161 (b) ₹184 (c) ₹23 (d) ₹92
6. 6.₹70 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹35 (b) ₹50 (c) ₹10 (d) ₹20
7. 7.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 15 days (c) 21 days (d) 13 days
8. 8.₹320 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹320 (b) ₹160 (c) ₹288 (d) ₹32
9. 9.If 7 pens cost ₹70, how much do 3 pens cost? (a) ₹66 (b) ₹30 (c) ₹40 (d) ₹210
10. 10.₹190 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹190 (b) ₹95 (c) ₹19 (d) ₹171
11. 11.If 8 kites cost ₹136, how much do 3 kites cost? (a) ₹51 (b) ₹68 (c) ₹408 (d) ₹131
12. 12.If 3 kites cost ₹51, how much do 6 kites cost? (a) ₹54 (b) ₹119 (c) ₹306 (d) ₹102
13. 13.₹348 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹203 (b) ₹174 (c) ₹145 (d) ₹29
14. 14.₹135 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹30 (b) ₹15 (c) ₹120 (d) ₹105
15. 15.₹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
16. 16.₹105 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹63 (b) ₹84 (c) ₹42 (d) ₹21
17. 17.If 3 pens cost ₹45, how much do 11 pens cost? (a) ₹495 (b) ₹180 (c) ₹165 (d) ₹53
18. 18.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 15 days (d) 4 days
19. 19.₹64 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹32 (b) ₹8 (c) ₹56 (d) ₹64
20. 20.₹55 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹11 (b) ₹22 (c) ₹44 (d) ₹33
21. 21.₹700 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹450 (b) ₹50 (c) ₹250 (d) ₹350
22. 22.If 4 notebooks cost ₹36, how much do 7 notebooks cost? (a) ₹39 (b) ₹252 (c) ₹63 (d) ₹72
23. 23.₹143 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹104 (b) ₹13 (c) ₹91 (d) ₹52
24. 24.₹650 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹250 (b) ₹325 (c) ₹400 (d) ₹50
25. 25.₹336 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹168 (b) ₹140 (c) ₹28 (d) ₹196
26. 26.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 4 days (d) 6 days
27. 27.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 11 days
28. 28.If 4 kites cost ₹72, how much do 5 kites cost? (a) ₹90 (b) ₹73 (c) ₹108 (d) ₹360
29. 29.7 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 14 days (c) 13 days (d) 11 days
30. 30.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 3 days (d) 4 days
31. 31.If 5 pens cost ₹35, how much do 7 pens cost? (a) ₹37 (b) ₹56 (c) ₹49 (d) ₹245
32. 32.If 3 pens cost ₹51, how much do 2 pens cost? (a) ₹50 (b) ₹51 (c) ₹34 (d) ₹102
33. 33.6 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 12 days (d) 13 days
34. 34.If 4 kites cost ₹84, how much do 8 kites cost? (a) ₹88 (b) ₹672 (c) ₹168 (d) ₹189
35. 35.If 3 pens cost ₹51, how much do 7 pens cost? (a) ₹55 (b) ₹119 (c) ₹136 (d) ₹357
36. 36.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 1 day
37. 37.If 8 pens cost ₹72, how much do 6 pens cost? (a) ₹432 (b) ₹63 (c) ₹70 (d) ₹54
38. 38.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 17 days (b) 7 days (c) 6 days (d) 8 days
39. 39.If 2 notebooks cost ₹44, how much do 3 notebooks cost? (a) ₹66 (b) ₹132 (c) ₹88 (d) ₹45
40. 40.₹88 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹88 (b) ₹22 (c) ₹44 (d) ₹66

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