Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 47 · 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.₹72 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹16 (b) ₹36 (c) ₹56 (d) ₹8
2. 2.If 5 pens cost ₹75, how much do 4 pens cost? (a) ₹74 (b) ₹75 (c) ₹300 (d) ₹60
3. 3.If 3 pens cost ₹27, how much do 4 pens cost? (a) ₹45 (b) ₹36 (c) ₹108 (d) ₹28
4. 4.₹196 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹49 (b) ₹196 (c) ₹147 (d) ₹98
5. 5.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 9 days (d) 4 days
6. 6.If 4 pens cost ₹20, how much do 9 pens cost? (a) ₹25 (b) ₹180 (c) ₹50 (d) ₹45
7. 7.If 9 notebooks cost ₹63, how much do 11 notebooks cost? (a) ₹693 (b) ₹65 (c) ₹77 (d) ₹84
8. 8.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 15 days (d) 14 days
9. 9.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 35 days (b) 19 days (c) 11 days (d) 36 days
10. 10.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 22 days (d) 23 days
11. 11.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 45 days (c) 21 days (d) 5 days
12. 12.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 1 day (d) 2 days
13. 13.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 1 day (d) 9 days
14. 14.If 2 pens cost ₹34, how much do 8 pens cost? (a) ₹40 (b) ₹136 (c) ₹272 (d) ₹153
15. 15.₹50 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹5 (b) ₹25 (c) ₹50 (d) ₹45
16. 16.If 2 notebooks cost ₹6, how much do 8 notebooks cost? (a) ₹27 (b) ₹12 (c) ₹48 (d) ₹24
17. 17.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 11 days (d) 8 days
18. 18.₹484 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹132 (b) ₹352 (c) ₹242 (d) ₹44
19. 19.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 34 days (c) 5 days (d) 33 days
20. 20.6 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 4 days (d) 16 days
21. 21.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 1 day (c) 15 days (d) 9 days
22. 22.If 8 mangoes cost ₹168, how much do 3 mangoes cost? (a) ₹504 (b) ₹163 (c) ₹84 (d) ₹63
23. 23.₹63 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹14 (b) ₹56 (c) ₹7 (d) ₹49
24. 24.₹440 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹440 (b) ₹44 (c) ₹220 (d) ₹396
25. 25.₹154 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹112 (b) ₹42 (c) ₹14 (d) ₹77
26. 26.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 10 days (c) 11 days (d) 7 days
27. 27.If 8 pens cost ₹48, how much do 9 pens cost? (a) ₹54 (b) ₹60 (c) ₹49 (d) ₹432
28. 28.If 2 pens cost ₹8, how much do 3 pens cost? (a) ₹24 (b) ₹16 (c) ₹9 (d) ₹12
29. 29.₹363 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹330 (b) ₹66 (c) ₹33 (d) ₹297
30. 30.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 6 days (c) 9 days (d) 8 days
31. 31.₹308 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹154 (b) ₹22 (c) ₹198 (d) ₹110
32. 32.If 3 kites cost ₹12, how much do 11 kites cost? (a) ₹48 (b) ₹132 (c) ₹44 (d) ₹20
33. 33.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 12 days (d) 7 days
34. 34.₹156 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹13 (b) ₹78 (c) ₹91 (d) ₹65
35. 35.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 3 days (c) 27 days (d) 15 days
36. 36.If 6 notebooks cost ₹30, how much do 11 notebooks cost? (a) ₹330 (b) ₹55 (c) ₹35 (d) ₹60
37. 37.₹196 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹84 (b) ₹28 (c) ₹98 (d) ₹112
38. 38.If 8 mangoes cost ₹64, how much do 5 mangoes cost? (a) ₹320 (b) ₹48 (c) ₹61 (d) ₹40
39. 39.₹112 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹16 (b) ₹56 (c) ₹80 (d) ₹32
40. 40.If 6 notebooks cost ₹72, how much do 12 notebooks cost? (a) ₹156 (b) ₹78 (c) ₹864 (d) ₹144

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