Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 386 · 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.₹51 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹34 (b) ₹35 (c) ₹51 (d) ₹17
2. 2.₹378 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹168 (b) ₹189 (c) ₹42 (d) ₹210
3. 3.₹138 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹46 (b) ₹92 (c) ₹138 (d) ₹69
4. 4.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 3 days (c) 12 days (d) 2 days
5. 5.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 10 days (d) 3 days
6. 6.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 20 days (d) 21 days
7. 7.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 2 days (d) 3 days
8. 8.₹378 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹189 (b) ₹294 (c) ₹42 (d) ₹84
9. 9.₹54 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹6 (b) ₹27 (c) ₹12 (d) ₹42
10. 10.If 6 pens cost ₹132, how much do 2 pens cost? (a) ₹264 (b) ₹66 (c) ₹44 (d) ₹128
11. 11.₹48 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹6 (b) ₹24 (c) ₹48 (d) ₹42
12. 12.If 4 mangoes cost ₹12, how much do 9 mangoes cost? (a) ₹27 (b) ₹17 (c) ₹30 (d) ₹108
13. 13.If 9 mangoes cost ₹108, how much do 5 mangoes cost? (a) ₹60 (b) ₹540 (c) ₹72 (d) ₹104
14. 14.If 8 notebooks cost ₹168, how much do 10 notebooks cost? (a) ₹231 (b) ₹210 (c) ₹1680 (d) ₹170
15. 15.If 8 notebooks cost ₹64, how much do 10 notebooks cost? (a) ₹88 (b) ₹640 (c) ₹66 (d) ₹80
16. 16.₹98 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹63 (b) ₹49 (c) ₹7 (d) ₹35
17. 17.₹72 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹30 (b) ₹42 (c) ₹6 (d) ₹36
18. 18.If 3 pens cost ₹39, how much do 10 pens cost? (a) ₹130 (b) ₹143 (c) ₹390 (d) ₹46
19. 19.₹301 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹215 (b) ₹258 (c) ₹43 (d) ₹86
20. 20.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 20 days (c) 14 days (d) 16 days
21. 21.₹451 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹41 (b) ₹205 (c) ₹287 (d) ₹246
22. 22.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 14 days (b) 5 days (c) 11 days (d) 15 days
23. 23.If 3 pens cost ₹33, how much do 9 pens cost? (a) ₹297 (b) ₹110 (c) ₹39 (d) ₹99
24. 24.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 7 days (d) 28 days
25. 25.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 9 days (d) 8 days
26. 26.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 11 days (d) 8 days
27. 27.4 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) 9 days (d) 8 days
28. 28.If 5 notebooks cost ₹35, how much do 7 notebooks cost? (a) ₹49 (b) ₹245 (c) ₹37 (d) ₹56
29. 29.If 2 kites cost ₹36, how much do 9 kites cost? (a) ₹324 (b) ₹162 (c) ₹180 (d) ₹43
30. 30.If 6 notebooks cost ₹42, how much do 4 notebooks cost? (a) ₹28 (b) ₹40 (c) ₹35 (d) ₹168
31. 31.If 2 mangoes cost ₹8, how much do 6 mangoes cost? (a) ₹28 (b) ₹48 (c) ₹24 (d) ₹12
32. 32.₹217 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹124 (b) ₹155 (c) ₹93 (d) ₹31
33. 33.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 34 days (b) 33 days (c) 17 days (d) 5 days
34. 34.If 5 pens cost ₹105, how much do 2 pens cost? (a) ₹63 (b) ₹102 (c) ₹210 (d) ₹42
35. 35.₹117 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹81 (b) ₹36 (c) ₹9 (d) ₹90
36. 36.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹49 (b) ₹42 (c) ₹7 (d) ₹35
37. 37.If 8 mangoes cost ₹144, how much do 2 mangoes cost? (a) ₹288 (b) ₹138 (c) ₹36 (d) ₹54
38. 38.If 7 pens cost ₹35, how much do 11 pens cost? (a) ₹60 (b) ₹385 (c) ₹39 (d) ₹55
39. 39.If 3 kites cost ₹60, how much do 7 kites cost? (a) ₹420 (b) ₹64 (c) ₹160 (d) ₹140
40. 40.₹528 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹48 (b) ₹288 (c) ₹240 (d) ₹264

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