Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 38 · 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. 1.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 22 days (c) 21 days (d) 13 days
2. 2.₹286 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹26 (b) ₹182 (c) ₹143 (d) ₹104
3. 3.If 7 kites cost ₹49, how much do 2 kites cost? (a) ₹98 (b) ₹44 (c) ₹21 (d) ₹14
4. 4.If 2 mangoes cost ₹6, how much do 3 mangoes cost? (a) ₹18 (b) ₹12 (c) ₹7 (d) ₹9
5. 5.₹658 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹329 (b) ₹423 (c) ₹47 (d) ₹235
6. 6.If 8 mangoes cost ₹176, how much do 12 mangoes cost? (a) ₹180 (b) ₹2112 (c) ₹286 (d) ₹264
7. 7.₹204 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹102 (b) ₹170 (c) ₹204 (d) ₹34
8. 8.₹84 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹21 (b) ₹63 (c) ₹42 (d) ₹84
9. 9.If 3 pens cost ₹72, how much do 12 pens cost? (a) ₹288 (b) ₹864 (c) ₹81 (d) ₹312
10. 10.If 2 notebooks cost ₹8, how much do 5 notebooks cost? (a) ₹24 (b) ₹40 (c) ₹20 (d) ₹11
11. 11.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 5 days (c) 9 days (d) 8 days
12. 12.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 6 days (d) 7 days
13. 13.If 2 kites cost ₹32, how much do 7 kites cost? (a) ₹37 (b) ₹224 (c) ₹112 (d) ₹128
14. 14.If 4 notebooks cost ₹28, how much do 5 notebooks cost? (a) ₹35 (b) ₹42 (c) ₹29 (d) ₹140
15. 15.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 27 days (b) 28 days (c) 19 days (d) 11 days
16. 16.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 8 days (d) 9 days
17. 17.If 4 notebooks cost ₹36, how much do 11 notebooks cost? (a) ₹99 (b) ₹43 (c) ₹396 (d) ₹108
18. 18.If 9 pens cost ₹126, how much do 11 pens cost? (a) ₹128 (b) ₹168 (c) ₹1386 (d) ₹154
19. 19.If 2 pens cost ₹16, how much do 3 pens cost? (a) ₹17 (b) ₹32 (c) ₹48 (d) ₹24
20. 20.₹78 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹78 (b) ₹39 (c) ₹65 (d) ₹13
21. 21.₹333 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹148 (b) ₹222 (c) ₹185 (d) ₹37
22. 22.₹490 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹175 (b) ₹245 (c) ₹315 (d) ₹35
23. 23.If 8 notebooks cost ₹56, how much do 3 notebooks cost? (a) ₹21 (b) ₹168 (c) ₹28 (d) ₹51
24. 24.If 7 mangoes cost ₹154, how much do 12 mangoes cost? (a) ₹1848 (b) ₹286 (c) ₹264 (d) ₹159
25. 25.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 6 days (d) 5 days
26. 26.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 15 days (d) 22 days
27. 27.₹230 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹161 (b) ₹69 (c) ₹115 (d) ₹23
28. 28.If 8 pens cost ₹64, how much do 9 pens cost? (a) ₹80 (b) ₹576 (c) ₹72 (d) ₹65
29. 29.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 23 days (b) 7 days (c) 15 days (d) 22 days
30. 30.₹230 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹138 (b) ₹115 (c) ₹92 (d) ₹46
31. 31.If 3 notebooks cost ₹69, how much do 5 notebooks cost? (a) ₹71 (b) ₹138 (c) ₹115 (d) ₹345
32. 32.If 9 mangoes cost ₹225, how much do 10 mangoes cost? (a) ₹2250 (b) ₹226 (c) ₹275 (d) ₹250
33. 33.₹60 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹60 (b) ₹10 (c) ₹50 (d) ₹30
34. 34.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 8 days (d) 9 days
35. 35.If 4 kites cost ₹36, how much do 6 kites cost? (a) ₹63 (b) ₹38 (c) ₹54 (d) ₹216
36. 36.If 6 pens cost ₹18, how much do 4 pens cost? (a) ₹12 (b) ₹16 (c) ₹72 (d) ₹15
37. 37.₹189 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹189 (b) ₹27 (c) ₹162 (d) ₹163
38. 38.4 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) 4 days (d) 3 days
39. 39.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 42 days (b) 10 days (c) 43 days (d) 18 days
40. 40.If 7 pens cost ₹140, how much do 8 pens cost? (a) ₹1120 (b) ₹160 (c) ₹141 (d) ₹180

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