Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 355 · 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 7 notebooks cost ₹161, how much do 3 notebooks cost? (a) ₹157 (b) ₹483 (c) ₹69 (d) ₹92
2. 2.₹135 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹75 (b) ₹60 (c) ₹90 (d) ₹15
3. 3.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 10 days (c) 16 days (d) 17 days
4. 4.If 4 pens cost ₹72, how much do 12 pens cost? (a) ₹80 (b) ₹864 (c) ₹234 (d) ₹216
5. 5.If 7 notebooks cost ₹105, how much do 2 notebooks cost? (a) ₹45 (b) ₹210 (c) ₹30 (d) ₹100
6. 6.If 5 kites cost ₹80, how much do 12 kites cost? (a) ₹960 (b) ₹208 (c) ₹87 (d) ₹192
7. 7.₹252 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹36 (b) ₹126 (c) ₹180 (d) ₹72
8. 8.If 8 pens cost ₹24, how much do 5 pens cost? (a) ₹18 (b) ₹15 (c) ₹21 (d) ₹120
9. 9.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 29 days (c) 28 days (d) 13 days
10. 10.If 9 pens cost ₹189, how much do 4 pens cost? (a) ₹84 (b) ₹756 (c) ₹105 (d) ₹184
11. 11.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 3 days (c) 8 days (d) 2 days
12. 12.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 3 days (d) 5 days
13. 13.If 3 kites cost ₹51, how much do 6 kites cost? (a) ₹119 (b) ₹306 (c) ₹54 (d) ₹102
14. 14.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 36 days (b) 6 days (c) 4 days (d) 18 days
15. 15.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 3 days (d) 9 days
16. 16.₹184 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹92 (b) ₹138 (c) ₹46 (d) ₹184
17. 17.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 16 days (c) 29 days (d) 28 days
18. 18.If 9 kites cost ₹198, how much do 8 kites cost? (a) ₹197 (b) ₹1584 (c) ₹198 (d) ₹176
19. 19.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 20 days (c) 8 days (d) 56 days
20. 20.If 6 pens cost ₹18, how much do 7 pens cost? (a) ₹24 (b) ₹19 (c) ₹126 (d) ₹21
21. 21.If 6 mangoes cost ₹54, how much do 3 mangoes cost? (a) ₹36 (b) ₹162 (c) ₹27 (d) ₹51
22. 22.If 7 notebooks cost ₹147, how much do 12 notebooks cost? (a) ₹252 (b) ₹1764 (c) ₹273 (d) ₹152
23. 23.₹328 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹41 (b) ₹164 (c) ₹123 (d) ₹205
24. 24.₹296 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹37 (b) ₹111 (c) ₹185 (d) ₹148
25. 25.₹460 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹322 (b) ₹138 (c) ₹46 (d) ₹230
26. 26.If 7 notebooks cost ₹140, how much do 10 notebooks cost? (a) ₹1400 (b) ₹200 (c) ₹220 (d) ₹143
27. 27.₹252 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹28 (b) ₹140 (c) ₹112 (d) ₹126
28. 28.₹102 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹102 (b) ₹68 (c) ₹34 (d) ₹51
29. 29.If 3 notebooks cost ₹48, how much do 7 notebooks cost? (a) ₹112 (b) ₹52 (c) ₹336 (d) ₹128
30. 30.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 18 days (d) 11 days
31. 31.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 3 days
32. 32.If 2 mangoes cost ₹46, how much do 3 mangoes cost? (a) ₹138 (b) ₹69 (c) ₹92 (d) ₹47
33. 33.₹420 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹42 (b) ₹378 (c) ₹420 (d) ₹210
34. 34.₹272 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹238 (b) ₹136 (c) ₹272 (d) ₹34
35. 35.If 8 kites cost ₹160, how much do 9 kites cost? (a) ₹180 (b) ₹1440 (c) ₹200 (d) ₹161
36. 36.If 6 mangoes cost ₹36, how much do 2 mangoes cost? (a) ₹72 (b) ₹32 (c) ₹12 (d) ₹18
37. 37.₹363 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹99 (b) ₹33 (c) ₹264 (d) ₹297
38. 38.₹308 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹56 (b) ₹28 (c) ₹252 (d) ₹154
39. 39.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 15 days (d) 14 days
40. 40.If 2 notebooks cost ₹38, how much do 3 notebooks cost? (a) ₹76 (b) ₹57 (c) ₹39 (d) ₹114

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