Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 607 · 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.₹154 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹126 (b) ₹28 (c) ₹77 (d) ₹14
2. 2.If 5 mangoes cost ₹75, how much do 4 mangoes cost? (a) ₹74 (b) ₹75 (c) ₹60 (d) ₹300
3. 3.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 18 days (c) 8 days (d) 9 days
4. 4.If 7 pens cost ₹49, how much do 8 pens cost? (a) ₹63 (b) ₹56 (c) ₹50 (d) ₹392
5. 5.₹162 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹81 (b) ₹90 (c) ₹18 (d) ₹72
6. 6.If 2 notebooks cost ₹8, how much do 4 notebooks cost? (a) ₹16 (b) ₹32 (c) ₹10 (d) ₹20
7. 7.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 13 days (b) 16 days (c) 15 days (d) 17 days
8. 8.₹215 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹172 (b) ₹43 (c) ₹86 (d) ₹129
9. 9.If 6 pens cost ₹126, how much do 2 pens cost? (a) ₹42 (b) ₹252 (c) ₹63 (d) ₹122
10. 10.₹441 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹294 (b) ₹196 (c) ₹49 (d) ₹245
11. 11.If 4 notebooks cost ₹88, how much do 10 notebooks cost? (a) ₹220 (b) ₹94 (c) ₹242 (d) ₹880
12. 12.₹135 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹15 (b) ₹121 (c) ₹120 (d) ₹135
13. 13.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 15 days (c) 35 days (d) 36 days
14. 14.₹442 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹34 (b) ₹272 (c) ₹170 (d) ₹221
15. 15.If 8 kites cost ₹56, how much do 4 kites cost? (a) ₹28 (b) ₹224 (c) ₹35 (d) ₹52
16. 16.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 4 days (d) 3 days
17. 17.If 6 notebooks cost ₹126, how much do 5 notebooks cost? (a) ₹126 (b) ₹630 (c) ₹125 (d) ₹105
18. 18.₹390 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹195 (b) ₹30 (c) ₹150 (d) ₹240
19. 19.If 8 kites cost ₹48, how much do 9 kites cost? (a) ₹432 (b) ₹54 (c) ₹49 (d) ₹60
20. 20.₹504 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹294 (b) ₹210 (c) ₹42 (d) ₹252
21. 21.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 1 day (c) 16 days (d) 9 days
22. 22.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 13 days (b) 8 days (c) 6 days (d) 7 days
23. 23.If 3 kites cost ₹60, how much do 11 kites cost? (a) ₹660 (b) ₹220 (c) ₹240 (d) ₹68
24. 24.₹224 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹192 (b) ₹224 (c) ₹32 (d) ₹112
25. 25.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 26 days (c) 27 days (d) 15 days
26. 26.₹25 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹10 (b) ₹5 (c) ₹15 (d) ₹20
27. 27.If 7 mangoes cost ₹42, how much do 10 mangoes cost? (a) ₹45 (b) ₹66 (c) ₹60 (d) ₹420
28. 28.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 63 days (c) 64 days (d) 7 days
29. 29.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 15 days (d) 20 days
30. 30.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 49 days (d) 19 days
31. 31.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 22 days (c) 13 days (d) 21 days
32. 32.7 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 11 days (c) 14 days (d) 13 days
33. 33.If 4 kites cost ₹100, how much do 11 kites cost? (a) ₹107 (b) ₹1100 (c) ₹275 (d) ₹300
34. 34.₹400 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹40 (b) ₹360 (c) ₹400 (d) ₹200
35. 35.If 7 kites cost ₹154, how much do 3 kites cost? (a) ₹66 (b) ₹150 (c) ₹462 (d) ₹88
36. 36.If 3 notebooks cost ₹15, how much do 4 notebooks cost? (a) ₹20 (b) ₹60 (c) ₹25 (d) ₹16
37. 37.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 18 days (c) 12 days (d) 19 days
38. 38.₹216 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹216 (b) ₹192 (c) ₹108 (d) ₹24
39. 39.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 3 days (d) 28 days
40. 40.If 8 kites cost ₹160, how much do 9 kites cost? (a) ₹1440 (b) ₹161 (c) ₹200 (d) ₹180

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