Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 640 · 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 9 notebooks cost ₹162, how much do 10 notebooks cost? (a) ₹198 (b) ₹1620 (c) ₹180 (d) ₹163
2. 2.₹55 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹40 (b) ₹5 (c) ₹20 (d) ₹35
3. 3.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 20 days (d) 5 days
4. 4.₹658 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹423 (b) ₹47 (c) ₹235 (d) ₹329
5. 5.9 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 19 days (b) 13 days (c) 3 days (d) 18 days
6. 6.₹270 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹135 (b) ₹27 (c) ₹270 (d) ₹243
7. 7.₹442 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹272 (b) ₹170 (c) ₹221 (d) ₹34
8. 8.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 2 days (c) 12 days (d) 3 days
9. 9.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 11 days (d) 13 days
10. 10.₹374 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹68 (b) ₹34 (c) ₹187 (d) ₹306
11. 11.If 4 kites cost ₹48, how much do 5 kites cost? (a) ₹72 (b) ₹49 (c) ₹60 (d) ₹240
12. 12.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 13 days (c) 28 days (d) 27 days
13. 13.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 1 day (c) 13 days (d) 21 days
14. 14.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 9 days (d) 10 days
15. 15.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 40 days (d) 39 days
16. 16.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 12 days (c) 9 days (d) 7 days
17. 17.₹185 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹37 (b) ₹111 (c) ₹74 (d) ₹148
18. 18.₹343 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹295 (b) ₹49 (c) ₹343 (d) ₹294
19. 19.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 10 days (c) 8 days (d) 11 days
20. 20.If 3 kites cost ₹27, how much do 2 kites cost? (a) ₹18 (b) ₹26 (c) ₹27 (d) ₹54
21. 21.₹231 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹189 (b) ₹21 (c) ₹168 (d) ₹63
22. 22.6 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
23. 23.₹117 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹36 (b) ₹81 (c) ₹9 (d) ₹90
24. 24.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 13 days
25. 25.If 3 pens cost ₹33, how much do 8 pens cost? (a) ₹99 (b) ₹264 (c) ₹38 (d) ₹88
26. 26.₹338 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹234 (b) ₹26 (c) ₹169 (d) ₹104
27. 27.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 19 days (c) 4 days (d) 2 days
28. 28.If 6 pens cost ₹54, how much do 12 pens cost? (a) ₹108 (b) ₹117 (c) ₹648 (d) ₹60
29. 29.₹15 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹5 (b) ₹11 (c) ₹15 (d) ₹10
30. 30.If 9 pens cost ₹216, how much do 10 pens cost? (a) ₹264 (b) ₹240 (c) ₹217 (d) ₹2160
31. 31.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 18 days (c) 6 days (d) 36 days
32. 32.If 9 kites cost ₹189, how much do 5 kites cost? (a) ₹126 (b) ₹945 (c) ₹185 (d) ₹105
33. 33.If 9 kites cost ₹198, how much do 10 kites cost? (a) ₹220 (b) ₹242 (c) ₹199 (d) ₹1980
34. 34.If 3 notebooks cost ₹51, how much do 8 notebooks cost? (a) ₹136 (b) ₹408 (c) ₹56 (d) ₹153
35. 35.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 17 days (d) 4 days
36. 36.If 7 pens cost ₹63, how much do 2 pens cost? (a) ₹126 (b) ₹27 (c) ₹58 (d) ₹18
37. 37.₹325 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹125 (b) ₹225 (c) ₹25 (d) ₹200
38. 38.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 2 days (c) 11 days (d) 3 days
39. 39.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 6 days (d) 5 days
40. 40.If 9 kites cost ₹27, how much do 10 kites cost? (a) ₹28 (b) ₹30 (c) ₹270 (d) ₹33

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