Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 85 · 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) 7 days (d) 40 days
2. 2.If 6 kites cost ₹150, how much do 2 kites cost? (a) ₹300 (b) ₹75 (c) ₹50 (d) ₹146
3. 3.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 29 days (b) 28 days (c) 13 days (d) 3 days
4. 4.If 9 mangoes cost ₹108, how much do 5 mangoes cost? (a) ₹60 (b) ₹72 (c) ₹540 (d) ₹104
5. 5.₹308 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹154 (b) ₹220 (c) ₹44 (d) ₹88
6. 6.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 25 days (b) 17 days (c) 9 days (d) 13 days
7. 7.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 28 days (d) 17 days
8. 8.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 15 days (c) 3 days (d) 37 days
9. 9.If 3 kites cost ₹69, how much do 5 kites cost? (a) ₹71 (b) ₹138 (c) ₹115 (d) ₹345
10. 10.₹650 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹50 (b) ₹325 (c) ₹400 (d) ₹250
11. 11.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 12 days (b) 9 days (c) 3 days (d) 4 days
12. 12.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 55 days (c) 54 days (d) 5 days
13. 13.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 24 days (c) 25 days (d) 4 days
14. 14.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 11 days
15. 15.If 2 kites cost ₹8, how much do 4 kites cost? (a) ₹16 (b) ₹32 (c) ₹20 (d) ₹10
16. 16.6 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 14 days (c) 2 days (d) 4 days
17. 17.₹180 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹180 (b) ₹90 (c) ₹20 (d) ₹160
18. 18.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 25 days (c) 13 days (d) 17 days
19. 19.If 8 pens cost ₹176, how much do 11 pens cost? (a) ₹242 (b) ₹179 (c) ₹1936 (d) ₹264
20. 20.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 36 days (b) 35 days (c) 19 days (d) 11 days
21. 21.₹130 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹10 (b) ₹40 (c) ₹65 (d) ₹90
22. 22.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 3 days (d) 4 days
23. 23.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 3 days (d) 2 days
24. 24.If 9 kites cost ₹198, how much do 7 kites cost? (a) ₹196 (b) ₹1386 (c) ₹154 (d) ₹176
25. 25.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 28 days (d) 27 days
26. 26.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 15 days (c) 14 days (d) 4 days
27. 27.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 15 days (c) 7 days (d) 6 days
28. 28.9 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 8 days (c) 9 days (d) 18 days
29. 29.₹161 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹46 (b) ₹138 (c) ₹23 (d) ₹115
30. 30.If 4 notebooks cost ₹80, how much do 5 notebooks cost? (a) ₹81 (b) ₹100 (c) ₹120 (d) ₹400
31. 31.If 9 notebooks cost ₹45, how much do 3 notebooks cost? (a) ₹20 (b) ₹39 (c) ₹15 (d) ₹135
32. 32.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 2 days (d) 1 day
33. 33.₹180 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹140 (b) ₹90 (c) ₹20 (d) ₹40
34. 34.If 4 mangoes cost ₹92, how much do 11 mangoes cost? (a) ₹253 (b) ₹99 (c) ₹276 (d) ₹1012
35. 35.If 2 notebooks cost ₹14, how much do 3 notebooks cost? (a) ₹15 (b) ₹42 (c) ₹28 (d) ₹21
36. 36.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 8 days (d) 9 days
37. 37.₹378 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹336 (b) ₹189 (c) ₹42 (d) ₹378
38. 38.₹384 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹192 (b) ₹48 (c) ₹336 (d) ₹384
39. 39.If 3 notebooks cost ₹48, how much do 4 notebooks cost? (a) ₹80 (b) ₹49 (c) ₹192 (d) ₹64
40. 40.If 8 mangoes cost ₹184, how much do 3 mangoes cost? (a) ₹179 (b) ₹552 (c) ₹92 (d) ₹69

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