Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 102 · 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.₹96 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹48 (b) ₹8 (c) ₹40 (d) ₹56
2. 2.₹408 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹204 (b) ₹238 (c) ₹34 (d) ₹170
3. 3.If 3 kites cost ₹60, how much do 9 kites cost? (a) ₹180 (b) ₹66 (c) ₹540 (d) ₹200
4. 4.₹287 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹205 (b) ₹82 (c) ₹41 (d) ₹246
5. 5.₹24 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹12 (b) ₹8 (c) ₹24 (d) ₹16
6. 6.₹351 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹195 (b) ₹39 (c) ₹156 (d) ₹234
7. 7.₹259 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹37 (b) ₹111 (c) ₹185 (d) ₹148
8. 8.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 9 days (d) 25 days
9. 9.If 4 mangoes cost ₹84, how much do 3 mangoes cost? (a) ₹252 (b) ₹84 (c) ₹63 (d) ₹83
10. 10.₹54 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹27 (b) ₹6 (c) ₹30 (d) ₹24
11. 11.If 7 pens cost ₹154, how much do 6 pens cost? (a) ₹153 (b) ₹924 (c) ₹154 (d) ₹132
12. 12.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 12 days (c) 8 days (d) 11 days
13. 13.₹78 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹24 (b) ₹6 (c) ₹54 (d) ₹39
14. 14.If 9 kites cost ₹36, how much do 11 kites cost? (a) ₹44 (b) ₹38 (c) ₹48 (d) ₹396
15. 15.If 3 kites cost ₹75, how much do 5 kites cost? (a) ₹150 (b) ₹375 (c) ₹77 (d) ₹125
16. 16.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 12 days (c) 16 days (d) 4 days
17. 17.If 7 kites cost ₹133, how much do 5 kites cost? (a) ₹131 (b) ₹114 (c) ₹665 (d) ₹95
18. 18.If 2 kites cost ₹10, how much do 6 kites cost? (a) ₹30 (b) ₹35 (c) ₹14 (d) ₹60
19. 19.₹198 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹36 (b) ₹162 (c) ₹18 (d) ₹99
20. 20.If 7 mangoes cost ₹21, how much do 8 mangoes cost? (a) ₹24 (b) ₹22 (c) ₹168 (d) ₹27
21. 21.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 10 days (c) 11 days (d) 12 days
22. 22.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 13 days (c) 7 days (d) 25 days
23. 23.If 6 notebooks cost ₹42, how much do 3 notebooks cost? (a) ₹39 (b) ₹126 (c) ₹28 (d) ₹21
24. 24.₹306 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹34 (b) ₹272 (c) ₹153 (d) ₹306
25. 25.If 3 pens cost ₹30, how much do 11 pens cost? (a) ₹38 (b) ₹110 (c) ₹120 (d) ₹330
26. 26.₹169 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹65 (b) ₹13 (c) ₹117 (d) ₹104
27. 27.If 2 pens cost ₹14, how much do 4 pens cost? (a) ₹28 (b) ₹16 (c) ₹35 (d) ₹56
28. 28.If 8 kites cost ₹192, how much do 9 kites cost? (a) ₹240 (b) ₹193 (c) ₹1728 (d) ₹216
29. 29.If 4 notebooks cost ₹60, how much do 11 notebooks cost? (a) ₹67 (b) ₹660 (c) ₹180 (d) ₹165
30. 30.₹279 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹248 (b) ₹31 (c) ₹249 (d) ₹279
31. 31.₹150 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹90 (b) ₹60 (c) ₹30 (d) ₹75
32. 32.If 3 kites cost ₹75, how much do 4 kites cost? (a) ₹100 (b) ₹300 (c) ₹76 (d) ₹125
33. 33.₹187 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹119 (b) ₹85 (c) ₹102 (d) ₹17
34. 34.If 4 kites cost ₹56, how much do 12 kites cost? (a) ₹672 (b) ₹64 (c) ₹182 (d) ₹168
35. 35.₹205 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹164 (b) ₹82 (c) ₹41 (d) ₹123
36. 36.₹40 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹40 (b) ₹10 (c) ₹20 (d) ₹30
37. 37.₹45 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹41 (b) ₹40 (c) ₹5 (d) ₹45
38. 38.₹96 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹48 (b) ₹64 (c) ₹32 (d) ₹96
39. 39.₹205 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹165 (b) ₹41 (c) ₹164 (d) ₹205
40. 40.If 9 notebooks cost ₹72, how much do 7 notebooks cost? (a) ₹504 (b) ₹56 (c) ₹70 (d) ₹64

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