Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 722 · 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.₹80 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹70 (b) ₹80 (c) ₹10 (d) ₹40
2. 2.If 7 kites cost ₹77, how much do 10 kites cost? (a) ₹80 (b) ₹121 (c) ₹110 (d) ₹770
3. 3.If 4 kites cost ₹40, how much do 9 kites cost? (a) ₹90 (b) ₹100 (c) ₹45 (d) ₹360
4. 4.₹133 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹57 (b) ₹76 (c) ₹19 (d) ₹95
5. 5.₹378 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹210 (b) ₹168 (c) ₹189 (d) ₹42
6. 6.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 13 days (c) 7 days (d) 6 days
7. 7.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 9 days (c) 13 days (d) 11 days
8. 8.If 2 notebooks cost ₹6, how much do 3 notebooks cost? (a) ₹9 (b) ₹7 (c) ₹18 (d) ₹12
9. 9.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 27 days (d) 26 days
10. 10.₹378 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹42 (b) ₹189 (c) ₹84 (d) ₹294
11. 11.₹228 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹114 (b) ₹95 (c) ₹133 (d) ₹19
12. 12.If 6 notebooks cost ₹48, how much do 10 notebooks cost? (a) ₹80 (b) ₹480 (c) ₹52 (d) ₹88
13. 13.If 3 notebooks cost ₹57, how much do 11 notebooks cost? (a) ₹65 (b) ₹627 (c) ₹228 (d) ₹209
14. 14.If 7 kites cost ₹140, how much do 8 kites cost? (a) ₹180 (b) ₹1120 (c) ₹160 (d) ₹141
15. 15.If 7 notebooks cost ₹77, how much do 5 notebooks cost? (a) ₹385 (b) ₹55 (c) ₹75 (d) ₹66
16. 16.If 5 pens cost ₹125, how much do 2 pens cost? (a) ₹122 (b) ₹75 (c) ₹50 (d) ₹250
17. 17.If 5 notebooks cost ₹40, how much do 9 notebooks cost? (a) ₹80 (b) ₹44 (c) ₹72 (d) ₹360
18. 18.₹168 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹14 (b) ₹98 (c) ₹84 (d) ₹70
19. 19.If 4 kites cost ₹40, how much do 3 kites cost? (a) ₹39 (b) ₹120 (c) ₹40 (d) ₹30
20. 20.If 4 pens cost ₹88, how much do 7 pens cost? (a) ₹91 (b) ₹154 (c) ₹616 (d) ₹176
21. 21.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 10 days (c) 17 days (d) 11 days
22. 22.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 5 days (d) 6 days
23. 23.₹352 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹32 (b) ₹128 (c) ₹224 (d) ₹176
24. 24.₹270 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹30 (b) ₹120 (c) ₹150 (d) ₹135
25. 25.If 9 mangoes cost ₹54, how much do 12 mangoes cost? (a) ₹648 (b) ₹78 (c) ₹57 (d) ₹72
26. 26.₹84 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹48 (b) ₹12 (c) ₹36 (d) ₹42
27. 27.If 7 pens cost ₹28, how much do 9 pens cost? (a) ₹30 (b) ₹40 (c) ₹36 (d) ₹252
28. 28.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 12 days (c) 24 days (d) 23 days
29. 29.3 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 5 days (d) 4 days
30. 30.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 27 days (b) 17 days (c) 26 days (d) 9 days
31. 31.₹540 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹45 (b) ₹315 (c) ₹270 (d) ₹225
32. 32.₹153 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹102 (b) ₹17 (c) ₹85 (d) ₹68
33. 33.If 5 pens cost ₹70, how much do 6 pens cost? (a) ₹84 (b) ₹98 (c) ₹71 (d) ₹420
34. 34.If 3 mangoes cost ₹45, how much do 6 mangoes cost? (a) ₹270 (b) ₹105 (c) ₹90 (d) ₹48
35. 35.If 7 notebooks cost ₹140, how much do 5 notebooks cost? (a) ₹138 (b) ₹700 (c) ₹120 (d) ₹100
36. 36.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 1 day (d) 11 days
37. 37.₹112 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹56 (b) ₹28 (c) ₹112 (d) ₹84
38. 38.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹9 (b) ₹72 (c) ₹45 (d) ₹81
39. 39.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 3 days (d) 5 days
40. 40.₹224 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹80 (b) ₹16 (c) ₹112 (d) ₹144

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