Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 467 · 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.₹105 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹90 (b) ₹15 (c) ₹91 (d) ₹105
2. 2.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 6 days (d) 7 days
3. 3.₹124 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹93 (b) ₹124 (c) ₹31 (d) ₹62
4. 4.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 4 days (d) 17 days
5. 5.If 7 pens cost ₹168, how much do 10 pens cost? (a) ₹240 (b) ₹171 (c) ₹264 (d) ₹1680
6. 6.₹312 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹273 (b) ₹312 (c) ₹39 (d) ₹156
7. 7.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 6 days (d) 2 days
8. 8.₹84 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹49 (b) ₹35 (c) ₹7 (d) ₹42
9. 9.If 8 kites cost ₹120, how much do 2 kites cost? (a) ₹45 (b) ₹30 (c) ₹240 (d) ₹114
10. 10.If 9 mangoes cost ₹207, how much do 11 mangoes cost? (a) ₹276 (b) ₹209 (c) ₹253 (d) ₹2277
11. 11.If 3 notebooks cost ₹75, how much do 2 notebooks cost? (a) ₹74 (b) ₹150 (c) ₹75 (d) ₹50
12. 12.If 9 kites cost ₹225, how much do 7 kites cost? (a) ₹175 (b) ₹200 (c) ₹223 (d) ₹1575
13. 13.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 11 days (d) 2 days
14. 14.₹360 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹30 (b) ₹150 (c) ₹210 (d) ₹180
15. 15.If 5 mangoes cost ₹125, how much do 3 mangoes cost? (a) ₹123 (b) ₹100 (c) ₹375 (d) ₹75
16. 16.₹484 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹44 (b) ₹242 (c) ₹396 (d) ₹88
17. 17.₹286 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹26 (b) ₹143 (c) ₹52 (d) ₹234
18. 18.₹376 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹376 (b) ₹329 (c) ₹47 (d) ₹188
19. 19.₹165 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹15 (b) ₹105 (c) ₹60 (d) ₹120
20. 20.If 2 kites cost ₹30, how much do 7 kites cost? (a) ₹120 (b) ₹210 (c) ₹35 (d) ₹105
21. 21.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 5 days
22. 22.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 2 days (c) 3 days (d) 12 days
23. 23.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 25 days (c) 9 days (d) 13 days
24. 24.If 6 kites cost ₹48, how much do 3 kites cost? (a) ₹24 (b) ₹144 (c) ₹45 (d) ₹32
25. 25.₹96 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹48 (b) ₹96 (c) ₹72 (d) ₹24
26. 26.If 7 kites cost ₹161, how much do 2 kites cost? (a) ₹69 (b) ₹156 (c) ₹322 (d) ₹46
27. 27.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 8 days (d) 9 days
28. 28.₹165 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹33 (b) ₹99 (c) ₹132 (d) ₹66
29. 29.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 15 days (c) 7 days (d) 6 days
30. 30.If 5 pens cost ₹50, how much do 3 pens cost? (a) ₹150 (b) ₹48 (c) ₹30 (d) ₹40
31. 31.If 5 notebooks cost ₹20, how much do 9 notebooks cost? (a) ₹40 (b) ₹36 (c) ₹24 (d) ₹180
32. 32.₹35 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹35 (b) ₹30 (c) ₹5 (d) ₹31
33. 33.₹418 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹38 (b) ₹190 (c) ₹209 (d) ₹228
34. 34.If 2 kites cost ₹42, how much do 3 kites cost? (a) ₹43 (b) ₹63 (c) ₹84 (d) ₹126
35. 35.₹45 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹5 (b) ₹25 (c) ₹20 (d) ₹30
36. 36.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 16 days (d) 6 days
37. 37.If 6 kites cost ₹30, how much do 10 kites cost? (a) ₹50 (b) ₹55 (c) ₹300 (d) ₹34
38. 38.₹45 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹9 (b) ₹36 (c) ₹45 (d) ₹37
39. 39.4 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) 9 days (d) 8 days
40. 40.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 3 days (d) 18 days

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