Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 353 · 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 8 pens cost ₹144, how much do 12 pens cost? (a) ₹1728 (b) ₹216 (c) ₹148 (d) ₹234
2. 2.₹287 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹287 (b) ₹247 (c) ₹246 (d) ₹41
3. 3.If 4 mangoes cost ₹40, how much do 5 mangoes cost? (a) ₹41 (b) ₹200 (c) ₹60 (d) ₹50
4. 4.If 6 notebooks cost ₹108, how much do 12 notebooks cost? (a) ₹114 (b) ₹1296 (c) ₹234 (d) ₹216
5. 5.₹264 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹264 (b) ₹132 (c) ₹44 (d) ₹220
6. 6.If 5 notebooks cost ₹65, how much do 12 notebooks cost? (a) ₹169 (b) ₹156 (c) ₹72 (d) ₹780
7. 7.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 10 days (c) 3 days (d) 2 days
8. 8.₹294 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹147 (b) ₹42 (c) ₹252 (d) ₹294
9. 9.₹517 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹47 (b) ₹188 (c) ₹329 (d) ₹376
10. 10.If 2 mangoes cost ₹42, how much do 3 mangoes cost? (a) ₹126 (b) ₹43 (c) ₹84 (d) ₹63
11. 11.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 18 days (b) 28 days (c) 10 days (d) 7 days
12. 12.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 40 days (d) 41 days
13. 13.4 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) 6 days (d) 4 days
14. 14.If 2 mangoes cost ₹38, how much do 7 mangoes cost? (a) ₹133 (b) ₹266 (c) ₹43 (d) ₹152
15. 15.If 6 pens cost ₹54, how much do 12 pens cost? (a) ₹117 (b) ₹648 (c) ₹60 (d) ₹108
16. 16.If 4 notebooks cost ₹52, how much do 3 notebooks cost? (a) ₹51 (b) ₹52 (c) ₹39 (d) ₹156
17. 17.If 5 mangoes cost ₹100, how much do 12 mangoes cost? (a) ₹240 (b) ₹107 (c) ₹1200 (d) ₹260
18. 18.₹104 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹39 (b) ₹13 (c) ₹52 (d) ₹65
19. 19.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 12 days (c) 15 days (d) 14 days
20. 20.₹85 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹17 (b) ₹34 (c) ₹68 (d) ₹51
21. 21.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 12 days (c) 19 days (d) 18 days
22. 22.4 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 14 days (d) 8 days
23. 23.₹200 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹40 (b) ₹100 (c) ₹200 (d) ₹160
24. 24.If 4 kites cost ₹92, how much do 5 kites cost? (a) ₹460 (b) ₹138 (c) ₹115 (d) ₹93
25. 25.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 19 days (c) 18 days (d) 11 days
26. 26.₹319 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹116 (b) ₹203 (c) ₹232 (d) ₹29
27. 27.If 2 pens cost ₹18, how much do 11 pens cost? (a) ₹198 (b) ₹99 (c) ₹27 (d) ₹108
28. 28.₹403 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹31 (b) ₹279 (c) ₹248 (d) ₹155
29. 29.If 2 pens cost ₹12, how much do 6 pens cost? (a) ₹72 (b) ₹42 (c) ₹36 (d) ₹16
30. 30.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 2 days (d) 3 days
31. 31.If 6 kites cost ₹150, how much do 2 kites cost? (a) ₹75 (b) ₹146 (c) ₹300 (d) ₹50
32. 32.If 2 pens cost ₹32, how much do 10 pens cost? (a) ₹40 (b) ₹160 (c) ₹320 (d) ₹176
33. 33.If 3 kites cost ₹75, how much do 4 kites cost? (a) ₹100 (b) ₹300 (c) ₹76 (d) ₹125
34. 34.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 4 days (d) 17 days
35. 35.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 4 days (c) 3 days (d) 27 days
36. 36.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 13 days (d) 12 days
37. 37.₹451 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹82 (b) ₹410 (c) ₹41 (d) ₹369
38. 38.If 2 kites cost ₹18, how much do 3 kites cost? (a) ₹54 (b) ₹27 (c) ₹36 (d) ₹19
39. 39.If 7 pens cost ₹119, how much do 8 pens cost? (a) ₹136 (b) ₹952 (c) ₹120 (d) ₹153
40. 40.If 8 notebooks cost ₹72, how much do 9 notebooks cost? (a) ₹648 (b) ₹73 (c) ₹81 (d) ₹90

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