Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 259 · 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.₹280 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹175 (b) ₹140 (c) ₹35 (d) ₹105
2. 2.If 6 notebooks cost ₹72, how much do 12 notebooks cost? (a) ₹156 (b) ₹144 (c) ₹78 (d) ₹864
3. 3.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 4 days (d) 3 days
4. 4.If 9 pens cost ₹90, how much do 10 pens cost? (a) ₹110 (b) ₹91 (c) ₹100 (d) ₹900
5. 5.₹196 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹14 (b) ₹98 (c) ₹126 (d) ₹70
6. 6.If 2 notebooks cost ₹40, how much do 11 notebooks cost? (a) ₹49 (b) ₹220 (c) ₹440 (d) ₹240
7. 7.If 6 kites cost ₹84, how much do 3 kites cost? (a) ₹252 (b) ₹56 (c) ₹81 (d) ₹42
8. 8.₹143 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹11 (b) ₹88 (c) ₹99 (d) ₹55
9. 9.₹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
10. 10.₹420 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹378 (b) ₹420 (c) ₹42 (d) ₹210
11. 11.If 7 mangoes cost ₹28, how much do 12 mangoes cost? (a) ₹336 (b) ₹48 (c) ₹33 (d) ₹52
12. 12.If 3 mangoes cost ₹27, how much do 5 mangoes cost? (a) ₹29 (b) ₹54 (c) ₹135 (d) ₹45
13. 13.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 9 days (d) 5 days
14. 14.₹221 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹85 (b) ₹136 (c) ₹153 (d) ₹17
15. 15.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 17 days (d) 8 days
16. 16.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 3 days (d) 4 days
17. 17.If 3 pens cost ₹12, how much do 8 pens cost? (a) ₹96 (b) ₹32 (c) ₹36 (d) ₹17
18. 18.If 5 kites cost ₹45, how much do 6 kites cost? (a) ₹46 (b) ₹270 (c) ₹54 (d) ₹63
19. 19.₹108 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹54 (b) ₹84 (c) ₹12 (d) ₹24
20. 20.₹247 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹19 (b) ₹152 (c) ₹95 (d) ₹171
21. 21.₹144 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹72 (b) ₹90 (c) ₹18 (d) ₹54
22. 22.₹60 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹6 (b) ₹42 (c) ₹18 (d) ₹30
23. 23.If 3 notebooks cost ₹42, how much do 7 notebooks cost? (a) ₹112 (b) ₹294 (c) ₹98 (d) ₹46
24. 24.If 4 pens cost ₹68, how much do 7 pens cost? (a) ₹136 (b) ₹476 (c) ₹119 (d) ₹71
25. 25.5 workers can build a wall in 12 days. How many days will 10 workers take, working at the same speed? (a) 17 days (b) 7 days (c) 24 days (d) 6 days
26. 26.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 17 days (c) 5 days (d) 44 days
27. 27.If 3 pens cost ₹30, how much do 4 pens cost? (a) ₹40 (b) ₹50 (c) ₹31 (d) ₹120
28. 28.If 6 notebooks cost ₹48, how much do 4 notebooks cost? (a) ₹46 (b) ₹40 (c) ₹192 (d) ₹32
29. 29.₹25 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹5 (b) ₹21 (c) ₹25 (d) ₹20
30. 30.If 4 pens cost ₹68, how much do 12 pens cost? (a) ₹816 (b) ₹76 (c) ₹221 (d) ₹204
31. 31.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 9 days
32. 32.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 13 days (c) 1 day (d) 21 days
33. 33.₹440 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹80 (b) ₹40 (c) ₹360 (d) ₹220
34. 34.If 4 mangoes cost ₹60, how much do 7 mangoes cost? (a) ₹63 (b) ₹420 (c) ₹105 (d) ₹120
35. 35.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 3 days (d) 4 days
36. 36.If 7 pens cost ₹112, how much do 3 pens cost? (a) ₹336 (b) ₹64 (c) ₹48 (d) ₹108
37. 37.If 2 mangoes cost ₹8, how much do 9 mangoes cost? (a) ₹15 (b) ₹72 (c) ₹36 (d) ₹40
38. 38.₹504 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹324 (b) ₹252 (c) ₹180 (d) ₹36
39. 39.9 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 15 days (c) 16 days (d) 9 days
40. 40.If 3 kites cost ₹39, how much do 10 kites cost? (a) ₹390 (b) ₹46 (c) ₹143 (d) ₹130

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