Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 946 · 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.₹374 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹136 (b) ₹187 (c) ₹34 (d) ₹238
2. 2.If 7 kites cost ₹119, how much do 6 kites cost? (a) ₹119 (b) ₹714 (c) ₹102 (d) ₹118
3. 3.₹48 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹24 (b) ₹6 (c) ₹18 (d) ₹30
4. 4.If 3 notebooks cost ₹60, how much do 4 notebooks cost? (a) ₹80 (b) ₹240 (c) ₹100 (d) ₹61
5. 5.₹120 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹105 (b) ₹60 (c) ₹15 (d) ₹120
6. 6.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 45 days (d) 5 days
7. 7.₹296 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹37 (b) ₹148 (c) ₹259 (d) ₹296
8. 8.₹406 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹261 (b) ₹203 (c) ₹145 (d) ₹29
9. 9.If 7 notebooks cost ₹35, how much do 2 notebooks cost? (a) ₹30 (b) ₹70 (c) ₹10 (d) ₹15
10. 10.₹176 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹96 (b) ₹16 (c) ₹88 (d) ₹80
11. 11.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 5 days (d) 25 days
12. 12.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 10 days (d) 8 days
13. 13.If 3 notebooks cost ₹69, how much do 2 notebooks cost? (a) ₹69 (b) ₹46 (c) ₹138 (d) ₹68
14. 14.If 2 notebooks cost ₹30, how much do 3 notebooks cost? (a) ₹45 (b) ₹60 (c) ₹90 (d) ₹31
15. 15.If 8 mangoes cost ₹176, how much do 9 mangoes cost? (a) ₹220 (b) ₹198 (c) ₹1584 (d) ₹177
16. 16.If 5 mangoes cost ₹60, how much do 6 mangoes cost? (a) ₹360 (b) ₹72 (c) ₹84 (d) ₹61
17. 17.If 3 kites cost ₹18, how much do 5 kites cost? (a) ₹90 (b) ₹36 (c) ₹20 (d) ₹30
18. 18.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 11 days (d) 3 days
19. 19.₹100 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹80 (b) ₹100 (c) ₹20 (d) ₹50
20. 20.If 7 kites cost ₹56, how much do 3 kites cost? (a) ₹32 (b) ₹24 (c) ₹52 (d) ₹168
21. 21.If 8 kites cost ₹64, how much do 10 kites cost? (a) ₹66 (b) ₹80 (c) ₹640 (d) ₹88
22. 22.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 17 days (d) 8 days
23. 23.₹150 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹25 (b) ₹75 (c) ₹150 (d) ₹125
24. 24.If 2 kites cost ₹18, how much do 12 kites cost? (a) ₹117 (b) ₹28 (c) ₹216 (d) ₹108
25. 25.9 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) 10 days (d) 8 days
26. 26.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 14 days (c) 21 days (d) 20 days
27. 27.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 21 days (d) 22 days
28. 28.₹272 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹102 (b) ₹34 (c) ₹136 (d) ₹170
29. 29.₹352 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹32 (b) ₹176 (c) ₹192 (d) ₹160
30. 30.If 4 notebooks cost ₹56, how much do 9 notebooks cost? (a) ₹61 (b) ₹140 (c) ₹126 (d) ₹504
31. 31.If 8 pens cost ₹72, how much do 11 pens cost? (a) ₹792 (b) ₹108 (c) ₹75 (d) ₹99
32. 32.If 5 notebooks cost ₹20, how much do 3 notebooks cost? (a) ₹12 (b) ₹18 (c) ₹60 (d) ₹16
33. 33.₹396 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹198 (b) ₹44 (c) ₹88 (d) ₹308
34. 34.₹405 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹315 (b) ₹45 (c) ₹90 (d) ₹360
35. 35.If 8 kites cost ₹200, how much do 11 kites cost? (a) ₹203 (b) ₹2200 (c) ₹275 (d) ₹300
36. 36.₹42 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹18 (b) ₹6 (c) ₹24 (d) ₹21
37. 37.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 15 days (c) 27 days (d) 3 days
38. 38.If 3 kites cost ₹75, how much do 2 kites cost? (a) ₹150 (b) ₹75 (c) ₹74 (d) ₹50
39. 39.If 5 kites cost ₹105, how much do 7 kites cost? (a) ₹735 (b) ₹147 (c) ₹107 (d) ₹168
40. 40.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 6 days (c) 8 days (d) 7 days

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