Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 832 · 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 notebooks cost ₹42, how much do 6 notebooks cost? (a) ₹126 (b) ₹46 (c) ₹147 (d) ₹252
2. 2.₹414 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹207 (b) ₹46 (c) ₹184 (d) ₹230
3. 3.If 4 kites cost ₹64, how much do 9 kites cost? (a) ₹576 (b) ₹144 (c) ₹160 (d) ₹69
4. 4.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 5 days (c) 4 days (d) 6 days
5. 5.8 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 14 days (c) 5 days (d) 20 days
6. 6.₹120 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹12 (b) ₹108 (c) ₹120 (d) ₹60
7. 7.₹230 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹46 (b) ₹138 (c) ₹115 (d) ₹92
8. 8.₹432 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹240 (b) ₹216 (c) ₹192 (d) ₹48
9. 9.₹490 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹490 (b) ₹441 (c) ₹49 (d) ₹245
10. 10.If 4 pens cost ₹44, how much do 2 pens cost? (a) ₹88 (b) ₹42 (c) ₹22 (d) ₹33
11. 11.6 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 12 days (c) 13 days (d) 11 days
12. 12.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 36 days (c) 37 days (d) 1 day
13. 13.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 6 days (d) 3 days
14. 14.₹275 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹25 (b) ₹50 (c) ₹250 (d) ₹225
15. 15.If 9 mangoes cost ₹99, how much do 11 mangoes cost? (a) ₹1089 (b) ₹101 (c) ₹132 (d) ₹121
16. 16.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 7 days (d) 15 days
17. 17.If 9 kites cost ₹216, how much do 4 kites cost? (a) ₹864 (b) ₹120 (c) ₹96 (d) ₹211
18. 18.6 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 19 days (d) 25 days
19. 19.₹132 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹66 (b) ₹12 (c) ₹24 (d) ₹108
20. 20.If 3 notebooks cost ₹63, how much do 7 notebooks cost? (a) ₹168 (b) ₹67 (c) ₹441 (d) ₹147
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) 12 days (d) 11 days
22. 22.₹45 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹5 (b) ₹30 (c) ₹20 (d) ₹25
23. 23.If 3 mangoes cost ₹39, how much do 10 mangoes cost? (a) ₹130 (b) ₹46 (c) ₹390 (d) ₹143
24. 24.₹374 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹34 (b) ₹306 (c) ₹187 (d) ₹68
25. 25.If 9 pens cost ₹198, how much do 11 pens cost? (a) ₹200 (b) ₹264 (c) ₹242 (d) ₹2178
26. 26.If 3 notebooks cost ₹30, how much do 4 notebooks cost? (a) ₹31 (b) ₹120 (c) ₹50 (d) ₹40
27. 27.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹44 (b) ₹8 (c) ₹48 (d) ₹40
28. 28.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 4 days (d) 15 days
29. 29.If 7 kites cost ₹140, how much do 2 kites cost? (a) ₹135 (b) ₹40 (c) ₹60 (d) ₹280
30. 30.If 7 kites cost ₹105, how much do 8 kites cost? (a) ₹840 (b) ₹135 (c) ₹106 (d) ₹120
31. 31.If 5 kites cost ₹70, how much do 11 kites cost? (a) ₹770 (b) ₹76 (c) ₹168 (d) ₹154
32. 32.If 3 mangoes cost ₹18, how much do 8 mangoes cost? (a) ₹23 (b) ₹54 (c) ₹144 (d) ₹48
33. 33.₹434 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹31 (b) ₹155 (c) ₹279 (d) ₹217
34. 34.If 3 mangoes cost ₹30, how much do 12 mangoes cost? (a) ₹39 (b) ₹130 (c) ₹360 (d) ₹120
35. 35.If 3 notebooks cost ₹9, how much do 2 notebooks cost? (a) ₹18 (b) ₹6 (c) ₹9 (d) ₹8
36. 36.₹168 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹70 (b) ₹98 (c) ₹84 (d) ₹14
37. 37.If 8 pens cost ₹192, how much do 7 pens cost? (a) ₹192 (b) ₹191 (c) ₹1344 (d) ₹168
38. 38.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 14 days (c) 3 days (d) 15 days
39. 39.₹45 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹36 (b) ₹45 (c) ₹9 (d) ₹37
40. 40.₹396 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹176 (b) ₹220 (c) ₹44 (d) ₹198

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