Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 400 · 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. 1.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 39 days (c) 40 days (d) 7 days
2. 2.₹550 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹250 (b) ₹275 (c) ₹50 (d) ₹300
3. 3.₹138 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹138 (b) ₹69 (c) ₹92 (d) ₹46
4. 4.If 8 kites cost ₹48, how much do 5 kites cost? (a) ₹36 (b) ₹30 (c) ₹45 (d) ₹240
5. 5.₹45 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹30 (b) ₹25 (c) ₹5 (d) ₹20
6. 6.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 24 days (c) 15 days (d) 9 days
7. 7.If 3 pens cost ₹45, how much do 10 pens cost? (a) ₹165 (b) ₹150 (c) ₹52 (d) ₹450
8. 8.₹36 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹9 (b) ₹18 (c) ₹36 (d) ₹27
9. 9.If 4 pens cost ₹68, how much do 5 pens cost? (a) ₹85 (b) ₹340 (c) ₹69 (d) ₹102
10. 10.If 2 kites cost ₹22, how much do 9 kites cost? (a) ₹29 (b) ₹110 (c) ₹198 (d) ₹99
11. 11.₹216 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹108 (b) ₹48 (c) ₹24 (d) ₹168
12. 12.If 2 mangoes cost ₹36, how much do 10 mangoes cost? (a) ₹198 (b) ₹180 (c) ₹360 (d) ₹44
13. 13.If 2 kites cost ₹22, how much do 11 kites cost? (a) ₹31 (b) ₹132 (c) ₹242 (d) ₹121
14. 14.₹230 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹138 (b) ₹92 (c) ₹46 (d) ₹115
15. 15.₹60 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹30 (b) ₹24 (c) ₹12 (d) ₹36
16. 16.₹135 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹15 (b) ₹90 (c) ₹60 (d) ₹75
17. 17.₹112 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹96 (b) ₹16 (c) ₹112 (d) ₹56
18. 18.If 9 pens cost ₹63, how much do 2 pens cost? (a) ₹21 (b) ₹126 (c) ₹14 (d) ₹56
19. 19.₹242 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹121 (b) ₹22 (c) ₹132 (d) ₹110
20. 20.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 10 days (d) 16 days
21. 21.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 4 days (d) 3 days
22. 22.If 4 kites cost ₹12, how much do 10 kites cost? (a) ₹33 (b) ₹18 (c) ₹30 (d) ₹120
23. 23.If 4 mangoes cost ₹52, how much do 3 mangoes cost? (a) ₹51 (b) ₹156 (c) ₹52 (d) ₹39
24. 24.₹273 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹235 (b) ₹39 (c) ₹273 (d) ₹234
25. 25.If 4 notebooks cost ₹16, how much do 5 notebooks cost? (a) ₹24 (b) ₹17 (c) ₹80 (d) ₹20
26. 26.₹180 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹90 (b) ₹20 (c) ₹180 (d) ₹160
27. 27.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 15 days (d) 4 days
28. 28.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 16 days (c) 13 days (d) 4 days
29. 29.9 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 18 days (c) 15 days (d) 9 days
30. 30.₹84 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹54 (b) ₹30 (c) ₹6 (d) ₹42
31. 31.₹24 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹12 (b) ₹24 (c) ₹6 (d) ₹18
32. 32.₹182 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹14 (b) ₹126 (c) ₹91 (d) ₹56
33. 33.₹441 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹245 (b) ₹49 (c) ₹196 (d) ₹294
34. 34.₹168 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹42 (b) ₹84 (c) ₹168 (d) ₹126
35. 35.₹546 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹168 (b) ₹273 (c) ₹378 (d) ₹42
36. 36.If 9 pens cost ₹144, how much do 5 pens cost? (a) ₹720 (b) ₹96 (c) ₹80 (d) ₹140
37. 37.If 8 notebooks cost ₹56, how much do 2 notebooks cost? (a) ₹21 (b) ₹14 (c) ₹50 (d) ₹112
38. 38.If 3 notebooks cost ₹18, how much do 9 notebooks cost? (a) ₹162 (b) ₹54 (c) ₹24 (d) ₹60
39. 39.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 60 days (c) 61 days (d) 21 days
40. 40.₹600 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹300 (b) ₹250 (c) ₹50 (d) ₹350

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