Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 331 · 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. 1.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 2 days (c) 32 days (d) 33 days
2. 2.If 7 pens cost ₹126, how much do 12 pens cost? (a) ₹234 (b) ₹131 (c) ₹1512 (d) ₹216
3. 3.₹220 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹88 (b) ₹132 (c) ₹44 (d) ₹110
4. 4.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 11 days
5. 5.If 4 mangoes cost ₹56, how much do 6 mangoes cost? (a) ₹84 (b) ₹98 (c) ₹58 (d) ₹336
6. 6.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 6 days (d) 4 days
7. 7.If 3 notebooks cost ₹9, how much do 4 notebooks cost? (a) ₹36 (b) ₹12 (c) ₹10 (d) ₹15
8. 8.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 14 days (b) 5 days (c) 3 days (d) 4 days
9. 9.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 8 days (c) 20 days (d) 56 days
10. 10.If 7 pens cost ₹140, how much do 10 pens cost? (a) ₹220 (b) ₹200 (c) ₹143 (d) ₹1400
11. 11.If 7 mangoes cost ₹168, how much do 2 mangoes cost? (a) ₹48 (b) ₹336 (c) ₹72 (d) ₹163
12. 12.If 8 mangoes cost ₹88, how much do 12 mangoes cost? (a) ₹132 (b) ₹92 (c) ₹143 (d) ₹1056
13. 13.₹198 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹18 (b) ₹99 (c) ₹72 (d) ₹126
14. 14.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 19 days (b) 28 days (c) 9 days (d) 7 days
15. 15.₹559 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹387 (b) ₹43 (c) ₹430 (d) ₹172
16. 16.₹315 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹271 (b) ₹315 (c) ₹270 (d) ₹45
17. 17.₹328 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹164 (b) ₹328 (c) ₹287 (d) ₹41
18. 18.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 1 day (c) 6 days (d) 8 days
19. 19.If 7 pens cost ₹175, how much do 3 pens cost? (a) ₹171 (b) ₹75 (c) ₹525 (d) ₹100
20. 20.₹72 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹42 (b) ₹36 (c) ₹6 (d) ₹30
21. 21.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 8 days (d) 12 days
22. 22.₹288 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹144 (b) ₹120 (c) ₹24 (d) ₹168
23. 23.₹351 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹108 (b) ₹243 (c) ₹27 (d) ₹270
24. 24.₹80 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹80 (b) ₹72 (c) ₹8 (d) ₹40
25. 25.₹235 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹188 (b) ₹94 (c) ₹47 (d) ₹141
26. 26.₹231 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹21 (b) ₹147 (c) ₹126 (d) ₹105
27. 27.If 4 kites cost ₹40, how much do 9 kites cost? (a) ₹100 (b) ₹360 (c) ₹45 (d) ₹90
28. 28.If 4 pens cost ₹92, how much do 5 pens cost? (a) ₹138 (b) ₹93 (c) ₹460 (d) ₹115
29. 29.₹54 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹54 (b) ₹18 (c) ₹36 (d) ₹27
30. 30.₹630 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹315 (b) ₹225 (c) ₹405 (d) ₹45
31. 31.₹462 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹42 (b) ₹294 (c) ₹168 (d) ₹231
32. 32.If 7 mangoes cost ₹21, how much do 12 mangoes cost? (a) ₹36 (b) ₹39 (c) ₹26 (d) ₹252
33. 33.₹216 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹24 (b) ₹96 (c) ₹108 (d) ₹120
34. 34.₹423 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹47 (b) ₹188 (c) ₹235 (d) ₹282
35. 35.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 7 days (d) 9 days
36. 36.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 34 days (b) 33 days (c) 15 days (d) 7 days
37. 37.If 6 kites cost ₹90, how much do 9 kites cost? (a) ₹93 (b) ₹810 (c) ₹135 (d) ₹150
38. 38.₹400 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹200 (b) ₹40 (c) ₹280 (d) ₹120
39. 39.If 9 kites cost ₹90, how much do 10 kites cost? (a) ₹100 (b) ₹900 (c) ₹91 (d) ₹110
40. 40.If 5 pens cost ₹75, how much do 7 pens cost? (a) ₹525 (b) ₹77 (c) ₹105 (d) ₹120

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