Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 418 · 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. 1.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 7 days (c) 13 days (d) 4 days
2. 2.₹102 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹51 (b) ₹102 (c) ₹34 (d) ₹68
3. 3.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 13 days (d) 17 days
4. 4.₹126 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹14 (b) ₹63 (c) ₹98 (d) ₹28
5. 5.₹144 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹128 (b) ₹144 (c) ₹16 (d) ₹72
6. 6.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 4 days (d) 5 days
7. 7.₹198 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹18 (b) ₹99 (c) ₹90 (d) ₹108
8. 8.If 3 notebooks cost ₹9, how much do 6 notebooks cost? (a) ₹12 (b) ₹18 (c) ₹54 (d) ₹21
9. 9.If 5 pens cost ₹105, how much do 4 pens cost? (a) ₹420 (b) ₹104 (c) ₹105 (d) ₹84
10. 10.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 27 days (d) 15 days
11. 11.₹70 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹10 (b) ₹20 (c) ₹50 (d) ₹35
12. 12.If 6 mangoes cost ₹150, how much do 7 mangoes cost? (a) ₹151 (b) ₹1050 (c) ₹200 (d) ₹175
13. 13.If 4 mangoes cost ₹40, how much do 12 mangoes cost? (a) ₹480 (b) ₹48 (c) ₹130 (d) ₹120
14. 14.₹108 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹9 (b) ₹54 (c) ₹63 (d) ₹45
15. 15.5 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
16. 16.₹253 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹115 (b) ₹23 (c) ₹161 (d) ₹138
17. 17.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 9 days (d) 6 days
18. 18.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 43 days (b) 42 days (c) 17 days (d) 7 days
19. 19.₹261 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹116 (b) ₹174 (c) ₹145 (d) ₹29
20. 20.₹170 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹85 (b) ₹34 (c) ₹170 (d) ₹136
21. 21.If 4 notebooks cost ₹52, how much do 8 notebooks cost? (a) ₹56 (b) ₹416 (c) ₹104 (d) ₹117
22. 22.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 28 days (d) 18 days
23. 23.If 6 mangoes cost ₹84, how much do 7 mangoes cost? (a) ₹112 (b) ₹85 (c) ₹588 (d) ₹98
24. 24.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 13 days (d) 25 days
25. 25.₹130 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹26 (b) ₹65 (c) ₹104 (d) ₹130
26. 26.If 2 pens cost ₹18, how much do 11 pens cost? (a) ₹99 (b) ₹198 (c) ₹108 (d) ₹27
27. 27.₹286 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹110 (b) ₹22 (c) ₹176 (d) ₹143
28. 28.If 4 kites cost ₹28, how much do 8 kites cost? (a) ₹224 (b) ₹32 (c) ₹63 (d) ₹56
29. 29.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 2 days (d) 3 days
30. 30.If 9 notebooks cost ₹216, how much do 6 notebooks cost? (a) ₹1296 (b) ₹213 (c) ₹144 (d) ₹168
31. 31.₹351 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹216 (b) ₹243 (c) ₹27 (d) ₹135
32. 32.If 8 pens cost ₹128, how much do 2 pens cost? (a) ₹256 (b) ₹48 (c) ₹122 (d) ₹32
33. 33.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 9 days (d) 5 days
34. 34.If 9 kites cost ₹207, how much do 2 kites cost? (a) ₹200 (b) ₹69 (c) ₹46 (d) ₹414
35. 35.₹242 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹121 (b) ₹198 (c) ₹44 (d) ₹22
36. 36.₹588 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹294 (b) ₹49 (c) ₹343 (d) ₹245
37. 37.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 10 days (c) 16 days (d) 11 days
38. 38.₹84 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹42 (b) ₹24 (c) ₹60 (d) ₹12
39. 39.If 2 mangoes cost ₹46, how much do 6 mangoes cost? (a) ₹161 (b) ₹276 (c) ₹50 (d) ₹138
40. 40.If 8 pens cost ₹144, how much do 9 pens cost? (a) ₹180 (b) ₹145 (c) ₹162 (d) ₹1296

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