Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 72 · 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 8 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 11 days (d) 9 days
2. 2.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 9 days (d) 4 days
3. 3.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 15 days (c) 27 days (d) 11 days
4. 4.₹238 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹238 (b) ₹204 (c) ₹119 (d) ₹34
5. 5.If 5 pens cost ₹45, how much do 8 pens cost? (a) ₹48 (b) ₹360 (c) ₹72 (d) ₹81
6. 6.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 13 days (b) 6 days (c) 7 days (d) 8 days
7. 7.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 14 days (c) 15 days (d) 11 days
8. 8.₹490 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹245 (b) ₹49 (c) ₹147 (d) ₹343
9. 9.₹91 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹63 (b) ₹7 (c) ₹28 (d) ₹70
10. 10.₹325 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹25 (b) ₹250 (c) ₹100 (d) ₹225
11. 11.9 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 45 days (c) 3 days (d) 46 days
12. 12.₹40 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹30 (b) ₹20 (c) ₹40 (d) ₹10
13. 13.If 3 pens cost ₹15, how much do 8 pens cost? (a) ₹40 (b) ₹120 (c) ₹45 (d) ₹20
14. 14.6 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 8 days (c) 12 days (d) 15 days
15. 15.If 5 pens cost ₹65, how much do 2 pens cost? (a) ₹62 (b) ₹26 (c) ₹130 (d) ₹39
16. 16.₹390 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹150 (b) ₹240 (c) ₹195 (d) ₹30
17. 17.If 7 notebooks cost ₹84, how much do 6 notebooks cost? (a) ₹504 (b) ₹84 (c) ₹83 (d) ₹72
18. 18.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 1 day (b) 2 days (c) 8 days (d) 3 days
19. 19.If 8 mangoes cost ₹48, how much do 12 mangoes cost? (a) ₹52 (b) ₹78 (c) ₹576 (d) ₹72
20. 20.₹147 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹127 (b) ₹126 (c) ₹21 (d) ₹147
21. 21.₹396 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹36 (b) ₹324 (c) ₹72 (d) ₹198
22. 22.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 45 days (b) 9 days (c) 21 days (d) 5 days
23. 23.If 5 mangoes cost ₹125, how much do 11 mangoes cost? (a) ₹300 (b) ₹131 (c) ₹275 (d) ₹1375
24. 24.If 2 pens cost ₹48, how much do 3 pens cost? (a) ₹72 (b) ₹144 (c) ₹96 (d) ₹49
25. 25.If 7 notebooks cost ₹63, how much do 9 notebooks cost? (a) ₹567 (b) ₹90 (c) ₹65 (d) ₹81
26. 26.If 4 kites cost ₹36, how much do 10 kites cost? (a) ₹99 (b) ₹42 (c) ₹360 (d) ₹90
27. 27.If 4 pens cost ₹60, how much do 5 pens cost? (a) ₹75 (b) ₹90 (c) ₹300 (d) ₹61
28. 28.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 19 days (c) 9 days (d) 4 days
29. 29.₹360 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹160 (b) ₹180 (c) ₹200 (d) ₹40
30. 30.₹351 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹156 (b) ₹39 (c) ₹195 (d) ₹234
31. 31.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 12 days (d) 14 days
32. 32.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 30 days (c) 12 days (d) 31 days
33. 33.If 5 kites cost ₹45, how much do 6 kites cost? (a) ₹63 (b) ₹46 (c) ₹270 (d) ₹54
34. 34.If 7 pens cost ₹42, how much do 2 pens cost? (a) ₹37 (b) ₹12 (c) ₹18 (d) ₹84
35. 35.If 8 kites cost ₹40, how much do 5 kites cost? (a) ₹200 (b) ₹37 (c) ₹25 (d) ₹30
36. 36.If 5 notebooks cost ₹40, how much do 11 notebooks cost? (a) ₹440 (b) ₹96 (c) ₹46 (d) ₹88
37. 37.If 6 pens cost ₹84, how much do 4 pens cost? (a) ₹336 (b) ₹56 (c) ₹70 (d) ₹82
38. 38.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 12 days (d) 16 days
39. 39.If 2 kites cost ₹12, how much do 6 kites cost? (a) ₹16 (b) ₹36 (c) ₹42 (d) ₹72
40. 40.If 3 pens cost ₹12, how much do 6 pens cost? (a) ₹15 (b) ₹24 (c) ₹28 (d) ₹72

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