Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 328 · 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.₹35 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹14 (b) ₹7 (c) ₹28 (d) ₹21
2. 2.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 26 days (c) 15 days (d) 27 days
3. 3.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 16 days (c) 4 days (d) 10 days
4. 4.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 17 days
5. 5.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 18 days (d) 15 days
6. 6.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 1 day (d) 3 days
7. 7.8 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 8 days (c) 18 days (d) 9 days
8. 8.If 8 kites cost ₹64, how much do 2 kites cost? (a) ₹128 (b) ₹24 (c) ₹58 (d) ₹16
9. 9.₹100 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹80 (b) ₹20 (c) ₹100 (d) ₹50
10. 10.₹430 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹430 (b) ₹43 (c) ₹215 (d) ₹387
11. 11.If 6 notebooks cost ₹60, how much do 5 notebooks cost? (a) ₹300 (b) ₹60 (c) ₹59 (d) ₹50
12. 12.If 2 mangoes cost ₹8, how much do 10 mangoes cost? (a) ₹44 (b) ₹80 (c) ₹40 (d) ₹16
13. 13.If 4 mangoes cost ₹76, how much do 12 mangoes cost? (a) ₹84 (b) ₹228 (c) ₹912 (d) ₹247
14. 14.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 41 days (b) 4 days (c) 16 days (d) 40 days
15. 15.6 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 6 days (c) 30 days (d) 31 days
16. 16.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 23 days (b) 7 days (c) 45 days (d) 5 days
17. 17.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 9 days (c) 7 days (d) 8 days
18. 18.₹286 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹143 (b) ₹22 (c) ₹198 (d) ₹88
19. 19.₹462 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹231 (b) ₹42 (c) ₹84 (d) ₹378
20. 20.If 3 mangoes cost ₹30, how much do 5 mangoes cost? (a) ₹60 (b) ₹150 (c) ₹50 (d) ₹32
21. 21.₹416 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹208 (b) ₹32 (c) ₹256 (d) ₹160
22. 22.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 35 days (c) 15 days (d) 36 days
23. 23.If 6 pens cost ₹96, how much do 3 pens cost? (a) ₹48 (b) ₹64 (c) ₹93 (d) ₹288
24. 24.₹60 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹25 (b) ₹30 (c) ₹5 (d) ₹35
25. 25.₹160 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹16 (b) ₹144 (c) ₹160 (d) ₹80
26. 26.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 22 days (c) 8 days (d) 23 days
27. 27.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 5 days (d) 4 days
28. 28.If 5 mangoes cost ₹100, how much do 9 mangoes cost? (a) ₹200 (b) ₹900 (c) ₹180 (d) ₹104
29. 29.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 7 days (d) 11 days
30. 30.₹245 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹105 (b) ₹175 (c) ₹35 (d) ₹140
31. 31.If 5 mangoes cost ₹75, how much do 8 mangoes cost? (a) ₹120 (b) ₹600 (c) ₹78 (d) ₹135
32. 32.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 15 days (d) 28 days
33. 33.If 2 notebooks cost ₹16, how much do 10 notebooks cost? (a) ₹80 (b) ₹88 (c) ₹160 (d) ₹24
34. 34.5 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) 20 days (d) 15 days
35. 35.If 9 mangoes cost ₹72, how much do 4 mangoes cost? (a) ₹67 (b) ₹32 (c) ₹40 (d) ₹288
36. 36.If 7 notebooks cost ₹21, how much do 8 notebooks cost? (a) ₹22 (b) ₹27 (c) ₹168 (d) ₹24
37. 37.If 3 notebooks cost ₹54, how much do 2 notebooks cost? (a) ₹53 (b) ₹108 (c) ₹36 (d) ₹54
38. 38.If 2 notebooks cost ₹44, how much do 10 notebooks cost? (a) ₹52 (b) ₹242 (c) ₹220 (d) ₹440
39. 39.If 8 kites cost ₹104, how much do 3 kites cost? (a) ₹99 (b) ₹312 (c) ₹52 (d) ₹39
40. 40.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 5 days (d) 2 days

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