Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 39 · 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. 1.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 11 days (c) 27 days (d) 26 days
2. 2.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 5 days (c) 34 days (d) 33 days
3. 3.If 4 mangoes cost ₹88, how much do 5 mangoes cost? (a) ₹89 (b) ₹132 (c) ₹110 (d) ₹440
4. 4.₹484 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹242 (b) ₹176 (c) ₹308 (d) ₹44
5. 5.If 4 notebooks cost ₹40, how much do 8 notebooks cost? (a) ₹320 (b) ₹80 (c) ₹90 (d) ₹44
6. 6.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 3 days (d) 9 days
7. 7.If 7 kites cost ₹133, how much do 12 kites cost? (a) ₹247 (b) ₹1596 (c) ₹228 (d) ₹138
8. 8.If 3 pens cost ₹33, how much do 5 pens cost? (a) ₹66 (b) ₹55 (c) ₹35 (d) ₹165
9. 9.₹231 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹189 (b) ₹21 (c) ₹42 (d) ₹210
10. 10.₹112 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹70 (b) ₹42 (c) ₹56 (d) ₹14
11. 11.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 4 days (d) 6 days
12. 12.₹210 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹105 (b) ₹30 (c) ₹180 (d) ₹210
13. 13.If 4 pens cost ₹16, how much do 12 pens cost? (a) ₹192 (b) ₹24 (c) ₹52 (d) ₹48
14. 14.If 6 notebooks cost ₹114, how much do 9 notebooks cost? (a) ₹190 (b) ₹117 (c) ₹1026 (d) ₹171
15. 15.If 8 notebooks cost ₹48, how much do 4 notebooks cost? (a) ₹30 (b) ₹192 (c) ₹24 (d) ₹44
16. 16.₹209 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹114 (b) ₹133 (c) ₹19 (d) ₹95
17. 17.₹154 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹56 (b) ₹14 (c) ₹77 (d) ₹98
18. 18.If 7 notebooks cost ₹49, how much do 3 notebooks cost? (a) ₹28 (b) ₹147 (c) ₹21 (d) ₹45
19. 19.₹72 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹72 (b) ₹9 (c) ₹36 (d) ₹63
20. 20.If 4 kites cost ₹32, how much do 5 kites cost? (a) ₹160 (b) ₹33 (c) ₹48 (d) ₹40
21. 21.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 10 days (b) 1 day (c) 8 days (d) 9 days
22. 22.If 3 pens cost ₹21, how much do 12 pens cost? (a) ₹84 (b) ₹30 (c) ₹91 (d) ₹252
23. 23.If 6 notebooks cost ₹114, how much do 8 notebooks cost? (a) ₹171 (b) ₹116 (c) ₹152 (d) ₹912
24. 24.If 9 notebooks cost ₹81, how much do 6 notebooks cost? (a) ₹54 (b) ₹63 (c) ₹486 (d) ₹78
25. 25.₹25 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹25 (b) ₹5 (c) ₹20 (d) ₹21
26. 26.If 4 pens cost ₹52, how much do 9 pens cost? (a) ₹468 (b) ₹130 (c) ₹117 (d) ₹57
27. 27.₹195 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹75 (b) ₹15 (c) ₹135 (d) ₹120
28. 28.If 8 pens cost ₹192, how much do 11 pens cost? (a) ₹288 (b) ₹195 (c) ₹2112 (d) ₹264
29. 29.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 4 days (c) 7 days (d) 3 days
30. 30.If 7 pens cost ₹77, how much do 11 pens cost? (a) ₹847 (b) ₹121 (c) ₹132 (d) ₹81
31. 31.If 3 mangoes cost ₹21, how much do 10 mangoes cost? (a) ₹28 (b) ₹70 (c) ₹77 (d) ₹210
32. 32.₹455 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹175 (b) ₹35 (c) ₹280 (d) ₹315
33. 33.If 6 kites cost ₹108, how much do 7 kites cost? (a) ₹109 (b) ₹144 (c) ₹126 (d) ₹756
34. 34.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 24 days (c) 6 days (d) 15 days
35. 35.If 4 kites cost ₹20, how much do 9 kites cost? (a) ₹180 (b) ₹25 (c) ₹45 (d) ₹50
36. 36.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 15 days (d) 14 days
37. 37.If 8 pens cost ₹40, how much do 10 pens cost? (a) ₹55 (b) ₹42 (c) ₹50 (d) ₹400
38. 38.If 8 notebooks cost ₹136, how much do 7 notebooks cost? (a) ₹136 (b) ₹119 (c) ₹952 (d) ₹135
39. 39.If 2 notebooks cost ₹44, how much do 9 notebooks cost? (a) ₹220 (b) ₹198 (c) ₹396 (d) ₹51
40. 40.₹99 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹63 (b) ₹36 (c) ₹9 (d) ₹72

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