Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 859 · 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.If 2 pens cost ₹30, how much do 9 pens cost? (a) ₹37 (b) ₹270 (c) ₹135 (d) ₹150
2. 2.If 5 pens cost ₹35, how much do 11 pens cost? (a) ₹41 (b) ₹84 (c) ₹385 (d) ₹77
3. 3.If 4 kites cost ₹24, how much do 11 kites cost? (a) ₹31 (b) ₹264 (c) ₹72 (d) ₹66
4. 4.₹120 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹120 (b) ₹108 (c) ₹12 (d) ₹60
5. 5.₹492 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹41 (b) ₹205 (c) ₹287 (d) ₹246
6. 6.If 6 notebooks cost ₹78, how much do 11 notebooks cost? (a) ₹156 (b) ₹83 (c) ₹858 (d) ₹143
7. 7.If 4 mangoes cost ₹68, how much do 9 mangoes cost? (a) ₹170 (b) ₹612 (c) ₹73 (d) ₹153
8. 8.₹440 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹360 (b) ₹80 (c) ₹40 (d) ₹220
9. 9.If 2 pens cost ₹48, how much do 12 pens cost? (a) ₹312 (b) ₹58 (c) ₹576 (d) ₹288
10. 10.₹144 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹54 (b) ₹90 (c) ₹18 (d) ₹72
11. 11.₹288 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹144 (b) ₹108 (c) ₹36 (d) ₹180
12. 12.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 27 days (c) 28 days (d) 17 days
13. 13.If 5 kites cost ₹70, how much do 12 kites cost? (a) ₹77 (b) ₹840 (c) ₹182 (d) ₹168
14. 14.₹230 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹115 (b) ₹161 (c) ₹23 (d) ₹69
15. 15.If 6 kites cost ₹72, how much do 7 kites cost? (a) ₹84 (b) ₹504 (c) ₹73 (d) ₹96
16. 16.If 9 kites cost ₹189, how much do 2 kites cost? (a) ₹182 (b) ₹42 (c) ₹63 (d) ₹378
17. 17.If 3 notebooks cost ₹75, how much do 7 notebooks cost? (a) ₹525 (b) ₹175 (c) ₹79 (d) ₹200
18. 18.If 2 pens cost ₹10, how much do 11 pens cost? (a) ₹110 (b) ₹55 (c) ₹19 (d) ₹60
19. 19.₹322 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹138 (b) ₹46 (c) ₹161 (d) ₹184
20. 20.₹198 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹99 (b) ₹18 (c) ₹36 (d) ₹162
21. 21.₹408 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹238 (b) ₹170 (c) ₹204 (d) ₹34
22. 22.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 6 days (c) 8 days (d) 7 days
23. 23.₹70 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹70 (b) ₹60 (c) ₹35 (d) ₹10
24. 24.If 7 mangoes cost ₹147, how much do 8 mangoes cost? (a) ₹148 (b) ₹189 (c) ₹168 (d) ₹1176
25. 25.If 8 pens cost ₹80, how much do 7 pens cost? (a) ₹80 (b) ₹560 (c) ₹70 (d) ₹79
26. 26.If 9 kites cost ₹225, how much do 4 kites cost? (a) ₹125 (b) ₹900 (c) ₹220 (d) ₹100
27. 27.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 3 days (c) 11 days (d) 21 days
28. 28.If 8 mangoes cost ₹56, how much do 12 mangoes cost? (a) ₹60 (b) ₹91 (c) ₹672 (d) ₹84
29. 29.₹369 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹328 (b) ₹82 (c) ₹287 (d) ₹41
30. 30.₹154 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹98 (b) ₹77 (c) ₹14 (d) ₹56
31. 31.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 13 days (d) 11 days
32. 32.₹576 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹288 (b) ₹336 (c) ₹48 (d) ₹240
33. 33.If 6 pens cost ₹126, how much do 7 pens cost? (a) ₹168 (b) ₹147 (c) ₹882 (d) ₹127
34. 34.₹98 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹84 (b) ₹49 (c) ₹14 (d) ₹98
35. 35.If 9 mangoes cost ₹117, how much do 6 mangoes cost? (a) ₹78 (b) ₹91 (c) ₹114 (d) ₹702
36. 36.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 19 days (d) 4 days
37. 37.₹363 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹99 (b) ₹264 (c) ₹33 (d) ₹297
38. 38.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 13 days (c) 21 days (d) 22 days
39. 39.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 14 days (d) 7 days
40. 40.₹288 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹252 (b) ₹144 (c) ₹288 (d) ₹36

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