Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 391 · 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. 1.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 3 days (c) 28 days (d) 29 days
2. 2.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 11 days (c) 8 days (d) 7 days
3. 3.₹225 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹25 (b) ₹201 (c) ₹200 (d) ₹225
4. 4.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 16 days (c) 13 days (d) 15 days
5. 5.₹208 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹64 (b) ₹144 (c) ₹104 (d) ₹16
6. 6.₹117 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹9 (b) ₹81 (c) ₹90 (d) ₹36
7. 7.₹54 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹9 (b) ₹54 (c) ₹45 (d) ₹27
8. 8.If 3 kites cost ₹27, how much do 4 kites cost? (a) ₹28 (b) ₹108 (c) ₹36 (d) ₹45
9. 9.If 2 kites cost ₹36, how much do 9 kites cost? (a) ₹324 (b) ₹180 (c) ₹162 (d) ₹43
10. 10.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 7 days (d) 4 days
11. 11.If 3 notebooks cost ₹54, how much do 11 notebooks cost? (a) ₹216 (b) ₹594 (c) ₹198 (d) ₹62
12. 12.₹54 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹27 (b) ₹6 (c) ₹54 (d) ₹48
13. 13.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 4 days (c) 7 days (d) 13 days
14. 14.₹208 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹104 (b) ₹16 (c) ₹128 (d) ₹80
15. 15.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 15 days (c) 6 days (d) 20 days
16. 16.₹325 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹25 (b) ₹225 (c) ₹125 (d) ₹200
17. 17.₹341 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹217 (b) ₹31 (c) ₹186 (d) ₹155
18. 18.₹468 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹180 (b) ₹234 (c) ₹288 (d) ₹36
19. 19.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 9 days (d) 5 days
20. 20.₹410 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹410 (b) ₹41 (c) ₹369 (d) ₹205
21. 21.If 7 notebooks cost ₹56, how much do 9 notebooks cost? (a) ₹58 (b) ₹80 (c) ₹504 (d) ₹72
22. 22.If 8 mangoes cost ₹136, how much do 3 mangoes cost? (a) ₹68 (b) ₹51 (c) ₹408 (d) ₹131
23. 23.₹160 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹64 (b) ₹80 (c) ₹32 (d) ₹96
24. 24.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 8 days (d) 6 days
25. 25.₹156 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹39 (b) ₹78 (c) ₹117 (d) ₹156
26. 26.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 10 days (d) 3 days
27. 27.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 8 days (c) 24 days (d) 6 days
28. 28.₹637 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹392 (b) ₹245 (c) ₹441 (d) ₹49
29. 29.If 4 notebooks cost ₹36, how much do 11 notebooks cost? (a) ₹99 (b) ₹43 (c) ₹108 (d) ₹396
30. 30.₹140 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹105 (b) ₹35 (c) ₹70 (d) ₹140
31. 31.₹216 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹48 (b) ₹108 (c) ₹24 (d) ₹168
32. 32.If 7 kites cost ₹168, how much do 8 kites cost? (a) ₹216 (b) ₹1344 (c) ₹169 (d) ₹192
33. 33.If 7 kites cost ₹63, how much do 6 kites cost? (a) ₹63 (b) ₹62 (c) ₹54 (d) ₹378
34. 34.9 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) 10 days (d) 8 days
35. 35.If 3 pens cost ₹48, how much do 2 pens cost? (a) ₹32 (b) ₹96 (c) ₹47 (d) ₹48
36. 36.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 21 days (c) 22 days (d) 13 days
37. 37.₹60 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹18 (b) ₹42 (c) ₹30 (d) ₹6
38. 38.₹84 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹30 (b) ₹6 (c) ₹42 (d) ₹54
39. 39.If 9 mangoes cost ₹54, how much do 4 mangoes cost? (a) ₹24 (b) ₹216 (c) ₹30 (d) ₹49
40. 40.If 2 notebooks cost ₹50, how much do 6 notebooks cost? (a) ₹175 (b) ₹150 (c) ₹300 (d) ₹54

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