Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 340 · 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 mangoes cost ₹12, how much do 11 mangoes cost? (a) ₹21 (b) ₹132 (c) ₹72 (d) ₹66
2. 2.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 14 days (d) 11 days
3. 3.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 3 days (d) 2 days
4. 4.₹329 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹282 (b) ₹235 (c) ₹94 (d) ₹47
5. 5.If 8 kites cost ₹200, how much do 3 kites cost? (a) ₹75 (b) ₹600 (c) ₹195 (d) ₹100
6. 6.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 11 days (d) 6 days
7. 7.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 13 days (c) 15 days (d) 21 days
8. 8.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 17 days (c) 16 days (d) 13 days
9. 9.6 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
10. 10.If 8 mangoes cost ₹136, how much do 2 mangoes cost? (a) ₹272 (b) ₹51 (c) ₹34 (d) ₹130
11. 11.₹84 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹6 (b) ₹30 (c) ₹42 (d) ₹54
12. 12.₹462 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹165 (b) ₹297 (c) ₹231 (d) ₹33
13. 13.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 9 days (d) 23 days
14. 14.If 9 mangoes cost ₹153, how much do 2 mangoes cost? (a) ₹34 (b) ₹51 (c) ₹306 (d) ₹146
15. 15.₹288 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹64 (b) ₹144 (c) ₹32 (d) ₹224
16. 16.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 27 days (d) 28 days
17. 17.₹165 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹33 (b) ₹99 (c) ₹132 (d) ₹66
18. 18.₹470 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹235 (b) ₹141 (c) ₹47 (d) ₹329
19. 19.₹390 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹240 (b) ₹195 (c) ₹30 (d) ₹150
20. 20.₹144 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹72 (b) ₹108 (c) ₹36 (d) ₹144
21. 21.If 9 kites cost ₹162, how much do 3 kites cost? (a) ₹486 (b) ₹54 (c) ₹156 (d) ₹72
22. 22.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 6 days (d) 9 days
23. 23.₹180 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹180 (b) ₹36 (c) ₹90 (d) ₹144
24. 24.₹115 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹115 (b) ₹93 (c) ₹92 (d) ₹23
25. 25.If 4 kites cost ₹100, how much do 7 kites cost? (a) ₹700 (b) ₹200 (c) ₹103 (d) ₹175
26. 26.₹42 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹30 (b) ₹21 (c) ₹6 (d) ₹12
27. 27.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 35 days (b) 11 days (c) 19 days (d) 36 days
28. 28.If 2 pens cost ₹12, how much do 5 pens cost? (a) ₹15 (b) ₹60 (c) ₹36 (d) ₹30
29. 29.9 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
30. 30.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 35 days (c) 11 days (d) 36 days
31. 31.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 3 days (d) 12 days
32. 32.₹185 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹148 (b) ₹185 (c) ₹37 (d) ₹149
33. 33.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 2 days (d) 1 day
34. 34.₹168 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹147 (b) ₹84 (c) ₹168 (d) ₹21
35. 35.If 6 notebooks cost ₹108, how much do 9 notebooks cost? (a) ₹162 (b) ₹180 (c) ₹111 (d) ₹972
36. 36.If 2 mangoes cost ₹32, how much do 11 mangoes cost? (a) ₹176 (b) ₹352 (c) ₹192 (d) ₹41
37. 37.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 8 days (d) 11 days
38. 38.If 5 kites cost ₹30, how much do 6 kites cost? (a) ₹42 (b) ₹180 (c) ₹36 (d) ₹31
39. 39.₹84 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹42 (b) ₹84 (c) ₹63 (d) ₹21
40. 40.If 7 kites cost ₹154, how much do 8 kites cost? (a) ₹198 (b) ₹155 (c) ₹1232 (d) ₹176

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