Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 761 · 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.₹300 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹30 (b) ₹150 (c) ₹90 (d) ₹210
2. 2.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 15 days (d) 13 days
3. 3.₹490 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹343 (b) ₹245 (c) ₹49 (d) ₹147
4. 4.If 4 kites cost ₹60, how much do 5 kites cost? (a) ₹61 (b) ₹300 (c) ₹90 (d) ₹75
5. 5.If 4 kites cost ₹72, how much do 9 kites cost? (a) ₹162 (b) ₹77 (c) ₹180 (d) ₹648
6. 6.₹182 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹52 (b) ₹91 (c) ₹26 (d) ₹130
7. 7.If 6 pens cost ₹84, how much do 3 pens cost? (a) ₹81 (b) ₹42 (c) ₹56 (d) ₹252
8. 8.₹208 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹128 (b) ₹104 (c) ₹16 (d) ₹80
9. 9.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 8 days (d) 13 days
10. 10.If 6 kites cost ₹120, how much do 5 kites cost? (a) ₹119 (b) ₹600 (c) ₹100 (d) ₹120
11. 11.₹336 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹168 (b) ₹24 (c) ₹216 (d) ₹120
12. 12.₹112 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹16 (b) ₹64 (c) ₹48 (d) ₹56
13. 13.₹473 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹43 (b) ₹215 (c) ₹258 (d) ₹301
14. 14.₹296 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹296 (b) ₹148 (c) ₹259 (d) ₹37
15. 15.₹455 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹35 (b) ₹315 (c) ₹350 (d) ₹140
16. 16.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 12 days (d) 6 days
17. 17.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 21 days (c) 19 days (d) 20 days
18. 18.₹264 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹33 (b) ₹264 (c) ₹231 (d) ₹132
19. 19.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 45 days (c) 21 days (d) 9 days
20. 20.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 6 days (d) 12 days
21. 21.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 61 days (d) 60 days
22. 22.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 10 days (c) 16 days (d) 1 day
23. 23.₹280 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹140 (b) ₹280 (c) ₹35 (d) ₹245
24. 24.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 12 days (c) 19 days (d) 18 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) 8 days (b) 6 days (c) 7 days (d) 3 days
26. 26.₹69 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹69 (b) ₹47 (c) ₹23 (d) ₹46
27. 27.₹168 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹70 (b) ₹98 (c) ₹84 (d) ₹14
28. 28.If 3 notebooks cost ₹75, how much do 12 notebooks cost? (a) ₹900 (b) ₹300 (c) ₹325 (d) ₹84
29. 29.₹77 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹70 (b) ₹14 (c) ₹7 (d) ₹63
30. 30.If 7 kites cost ₹105, how much do 10 kites cost? (a) ₹165 (b) ₹1050 (c) ₹150 (d) ₹108
31. 31.If 4 kites cost ₹40, how much do 11 kites cost? (a) ₹47 (b) ₹110 (c) ₹440 (d) ₹120
32. 32.₹105 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹45 (b) ₹75 (c) ₹15 (d) ₹60
33. 33.If 3 pens cost ₹54, how much do 7 pens cost? (a) ₹126 (b) ₹58 (c) ₹378 (d) ₹144
34. 34.₹406 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹29 (b) ₹261 (c) ₹145 (d) ₹203
35. 35.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 3 days (d) 2 days
36. 36.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 3 days (d) 6 days
37. 37.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 37 days (b) 1 day (c) 36 days (d) 15 days
38. 38.If 2 kites cost ₹46, how much do 11 kites cost? (a) ₹55 (b) ₹506 (c) ₹253 (d) ₹276
39. 39.₹405 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹45 (b) ₹180 (c) ₹225 (d) ₹270
40. 40.If 4 mangoes cost ₹32, how much do 3 mangoes cost? (a) ₹96 (b) ₹32 (c) ₹24 (d) ₹31

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