Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 58 · 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.₹88 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹56 (b) ₹32 (c) ₹44 (d) ₹8
2. 2.If 8 kites cost ₹72, how much do 12 kites cost? (a) ₹117 (b) ₹76 (c) ₹864 (d) ₹108
3. 3.If 4 pens cost ₹16, how much do 8 pens cost? (a) ₹128 (b) ₹20 (c) ₹36 (d) ₹32
4. 4.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 4 days (d) 1 day
5. 5.8 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 14 days (c) 20 days (d) 6 days
6. 6.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 10 days (d) 16 days
7. 7.₹165 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹15 (b) ₹150 (c) ₹135 (d) ₹30
8. 8.If 9 pens cost ₹153, how much do 3 pens cost? (a) ₹459 (b) ₹68 (c) ₹147 (d) ₹51
9. 9.₹484 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹264 (b) ₹220 (c) ₹44 (d) ₹242
10. 10.₹420 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹378 (b) ₹420 (c) ₹42 (d) ₹210
11. 11.If 2 pens cost ₹36, how much do 4 pens cost? (a) ₹144 (b) ₹72 (c) ₹90 (d) ₹38
12. 12.₹245 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹35 (b) ₹140 (c) ₹105 (d) ₹175
13. 13.₹504 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹210 (b) ₹294 (c) ₹42 (d) ₹252
14. 14.If 3 notebooks cost ₹18, how much do 10 notebooks cost? (a) ₹180 (b) ₹66 (c) ₹25 (d) ₹60
15. 15.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 6 days (c) 4 days (d) 36 days
16. 16.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 27 days (d) 26 days
17. 17.If 5 mangoes cost ₹25, how much do 4 mangoes cost? (a) ₹25 (b) ₹24 (c) ₹100 (d) ₹20
18. 18.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 3 days (d) 7 days
19. 19.6 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 14 days (b) 16 days (c) 19 days (d) 18 days
20. 20.If 3 kites cost ₹30, how much do 12 kites cost? (a) ₹120 (b) ₹360 (c) ₹39 (d) ₹130
21. 21.₹224 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹32 (b) ₹112 (c) ₹128 (d) ₹96
22. 22.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 1 day (c) 8 days (d) 7 days
23. 23.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 9 days (d) 21 days
24. 24.If 9 notebooks cost ₹54, how much do 5 notebooks cost? (a) ₹50 (b) ₹36 (c) ₹30 (d) ₹270
25. 25.5 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 21 days (c) 20 days (d) 10 days
26. 26.₹234 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹234 (b) ₹117 (c) ₹26 (d) ₹208
27. 27.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 12 days (d) 4 days
28. 28.If 7 notebooks cost ₹175, how much do 2 notebooks cost? (a) ₹350 (b) ₹75 (c) ₹170 (d) ₹50
29. 29.If 3 notebooks cost ₹21, how much do 4 notebooks cost? (a) ₹84 (b) ₹28 (c) ₹35 (d) ₹22
30. 30.₹184 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹115 (b) ₹23 (c) ₹69 (d) ₹92
31. 31.₹275 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹200 (b) ₹25 (c) ₹100 (d) ₹175
32. 32.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 17 days (c) 13 days (d) 16 days
33. 33.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 6 days (c) 10 days (d) 7 days
34. 34.9 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) 33 days (d) 5 days
35. 35.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 26 days (d) 11 days
36. 36.8 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) 7 days (d) 9 days
37. 37.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 17 days (c) 16 days (d) 10 days
38. 38.If 2 mangoes cost ₹36, how much do 8 mangoes cost? (a) ₹162 (b) ₹288 (c) ₹144 (d) ₹42
39. 39.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 18 days (b) 3 days (c) 5 days (d) 4 days
40. 40.₹176 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹132 (b) ₹176 (c) ₹44 (d) ₹88

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