Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 547 · 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.₹165 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹120 (b) ₹15 (c) ₹105 (d) ₹60
2. 2.6 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 21 days (b) 16 days (c) 12 days (d) 22 days
3. 3.₹600 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹300 (b) ₹50 (c) ₹250 (d) ₹350
4. 4.If 6 pens cost ₹66, how much do 7 pens cost? (a) ₹462 (b) ₹77 (c) ₹67 (d) ₹88
5. 5.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 2 days (c) 3 days (d) 4 days
6. 6.If 2 notebooks cost ₹42, how much do 7 notebooks cost? (a) ₹47 (b) ₹147 (c) ₹168 (d) ₹294
7. 7.If 9 notebooks cost ₹171, how much do 11 notebooks cost? (a) ₹209 (b) ₹173 (c) ₹228 (d) ₹1881
8. 8.If 4 kites cost ₹56, how much do 9 kites cost? (a) ₹126 (b) ₹61 (c) ₹504 (d) ₹140
9. 9.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 17 days (d) 9 days
10. 10.9 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 17 days (c) 46 days (d) 3 days
11. 11.₹451 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹369 (b) ₹41 (c) ₹123 (d) ₹328
12. 12.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 25 days (d) 16 days
13. 13.If 2 notebooks cost ₹18, how much do 5 notebooks cost? (a) ₹90 (b) ₹54 (c) ₹21 (d) ₹45
14. 14.₹35 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹10 (b) ₹30 (c) ₹25 (d) ₹5
15. 15.₹387 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹258 (b) ₹215 (c) ₹172 (d) ₹43
16. 16.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 22 days (c) 21 days (d) 3 days
17. 17.If 6 mangoes cost ₹18, how much do 3 mangoes cost? (a) ₹54 (b) ₹9 (c) ₹15 (d) ₹12
18. 18.₹108 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹72 (b) ₹108 (c) ₹54 (d) ₹36
19. 19.If 3 kites cost ₹36, how much do 10 kites cost? (a) ₹132 (b) ₹360 (c) ₹120 (d) ₹43
20. 20.If 7 pens cost ₹154, how much do 9 pens cost? (a) ₹220 (b) ₹1386 (c) ₹198 (d) ₹156
21. 21.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 6 days (c) 10 days (d) 7 days
22. 22.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 13 days (d) 26 days
23. 23.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 2 days (d) 1 day
24. 24.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 4 days (d) 7 days
25. 25.If 8 mangoes cost ₹32, how much do 11 mangoes cost? (a) ₹44 (b) ₹352 (c) ₹48 (d) ₹35
26. 26.₹56 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹56 (b) ₹48 (c) ₹8 (d) ₹28
27. 27.₹144 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹72 (b) ₹120 (c) ₹144 (d) ₹24
28. 28.If 2 kites cost ₹18, how much do 4 kites cost? (a) ₹20 (b) ₹36 (c) ₹45 (d) ₹72
29. 29.If 5 notebooks cost ₹90, how much do 4 notebooks cost? (a) ₹360 (b) ₹72 (c) ₹89 (d) ₹90
30. 30.If 2 mangoes cost ₹32, how much do 10 mangoes cost? (a) ₹160 (b) ₹40 (c) ₹176 (d) ₹320
31. 31.If 2 kites cost ₹30, how much do 4 kites cost? (a) ₹60 (b) ₹120 (c) ₹75 (d) ₹32
32. 32.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 9 days (d) 5 days
33. 33.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 3 days (c) 2 days (d) 12 days
34. 34.6 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 14 days (b) 16 days (c) 19 days (d) 18 days
35. 35.If 2 notebooks cost ₹10, how much do 5 notebooks cost? (a) ₹13 (b) ₹30 (c) ₹50 (d) ₹25
36. 36.₹286 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹143 (b) ₹104 (c) ₹26 (d) ₹182
37. 37.₹351 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹243 (b) ₹27 (c) ₹216 (d) ₹135
38. 38.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 12 days (c) 19 days (d) 6 days
39. 39.If 9 mangoes cost ₹63, how much do 10 mangoes cost? (a) ₹77 (b) ₹630 (c) ₹64 (d) ₹70
40. 40.If 7 notebooks cost ₹21, how much do 6 notebooks cost? (a) ₹21 (b) ₹126 (c) ₹20 (d) ₹18

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