Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 988 · 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.₹161 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹23 (b) ₹115 (c) ₹69 (d) ₹92
2. 2.₹300 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹150 (b) ₹250 (c) ₹50 (d) ₹300
3. 3.₹279 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹31 (b) ₹248 (c) ₹62 (d) ₹217
4. 4.₹195 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹117 (b) ₹78 (c) ₹39 (d) ₹156
5. 5.₹216 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹24 (b) ₹108 (c) ₹96 (d) ₹120
6. 6.₹143 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹91 (b) ₹65 (c) ₹78 (d) ₹13
7. 7.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 3 days (d) 4 days
8. 8.₹495 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹180 (b) ₹360 (c) ₹315 (d) ₹45
9. 9.₹30 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹15 (b) ₹12 (c) ₹18 (d) ₹6
10. 10.If 2 pens cost ₹16, how much do 11 pens cost? (a) ₹176 (b) ₹25 (c) ₹96 (d) ₹88
11. 11.If 6 mangoes cost ₹84, how much do 10 mangoes cost? (a) ₹840 (b) ₹154 (c) ₹88 (d) ₹140
12. 12.If 2 notebooks cost ₹46, how much do 10 notebooks cost? (a) ₹460 (b) ₹54 (c) ₹253 (d) ₹230
13. 13.₹110 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹70 (b) ₹40 (c) ₹55 (d) ₹10
14. 14.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 3 days
15. 15.₹360 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹40 (b) ₹320 (c) ₹360 (d) ₹180
16. 16.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 28 days (c) 29 days (d) 1 day
17. 17.If 8 pens cost ₹152, how much do 3 pens cost? (a) ₹57 (b) ₹76 (c) ₹456 (d) ₹147
18. 18.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 24 days (b) 9 days (c) 6 days (d) 15 days
19. 19.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 16 days (d) 12 days
20. 20.If 9 kites cost ₹189, how much do 3 kites cost? (a) ₹183 (b) ₹567 (c) ₹63 (d) ₹84
21. 21.₹99 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹11 (b) ₹77 (c) ₹88 (d) ₹22
22. 22.₹162 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹162 (b) ₹135 (c) ₹81 (d) ₹27
23. 23.₹126 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹21 (b) ₹105 (c) ₹63 (d) ₹126
24. 24.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 15 days (d) 27 days
25. 25.If 6 kites cost ₹90, how much do 5 kites cost? (a) ₹450 (b) ₹90 (c) ₹89 (d) ₹75
26. 26.If 6 notebooks cost ₹84, how much do 8 notebooks cost? (a) ₹112 (b) ₹672 (c) ₹86 (d) ₹126
27. 27.If 6 pens cost ₹42, how much do 2 pens cost? (a) ₹21 (b) ₹84 (c) ₹38 (d) ₹14
28. 28.If 9 mangoes cost ₹207, how much do 3 mangoes cost? (a) ₹69 (b) ₹621 (c) ₹201 (d) ₹92
29. 29.₹90 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹45 (b) ₹63 (c) ₹27 (d) ₹9
30. 30.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 15 days
31. 31.If 9 kites cost ₹171, how much do 6 kites cost? (a) ₹114 (b) ₹1026 (c) ₹168 (d) ₹133
32. 32.₹99 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹54 (b) ₹9 (c) ₹63 (d) ₹45
33. 33.5 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) 6 days (d) 3 days
34. 34.If 8 notebooks cost ₹176, how much do 12 notebooks cost? (a) ₹2112 (b) ₹180 (c) ₹264 (d) ₹286
35. 35.If 3 notebooks cost ₹75, how much do 4 notebooks cost? (a) ₹300 (b) ₹100 (c) ₹76 (d) ₹125
36. 36.If 4 kites cost ₹56, how much do 8 kites cost? (a) ₹448 (b) ₹60 (c) ₹126 (d) ₹112
37. 37.If 6 pens cost ₹48, how much do 10 pens cost? (a) ₹52 (b) ₹80 (c) ₹480 (d) ₹88
38. 38.If 6 kites cost ₹126, how much do 9 kites cost? (a) ₹210 (b) ₹1134 (c) ₹129 (d) ₹189
39. 39.₹100 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹50 (b) ₹10 (c) ₹100 (d) ₹90
40. 40.If 3 mangoes cost ₹9, how much do 4 mangoes cost? (a) ₹12 (b) ₹15 (c) ₹10 (d) ₹36

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