Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 20 · 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.If 4 pens cost ₹40, how much do 7 pens cost? (a) ₹280 (b) ₹43 (c) ₹70 (d) ₹80
2. 2.If 6 kites cost ₹24, how much do 7 kites cost? (a) ₹25 (b) ₹32 (c) ₹168 (d) ₹28
3. 3.If 3 pens cost ₹57, how much do 4 pens cost? (a) ₹76 (b) ₹228 (c) ₹95 (d) ₹58
4. 4.₹308 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹84 (b) ₹224 (c) ₹154 (d) ₹28
5. 5.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 21 days (b) 9 days (c) 5 days (d) 45 days
6. 6.If 9 kites cost ₹72, how much do 3 kites cost? (a) ₹24 (b) ₹32 (c) ₹66 (d) ₹216
7. 7.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 43 days (b) 20 days (c) 8 days (d) 42 days
8. 8.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 16 days (c) 29 days (d) 8 days
9. 9.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 29 days (b) 13 days (c) 1 day (d) 28 days
10. 10.₹150 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹75 (b) ₹60 (c) ₹30 (d) ₹90
11. 11.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 4 days (d) 6 days
12. 12.If 7 mangoes cost ₹63, how much do 8 mangoes cost? (a) ₹64 (b) ₹504 (c) ₹72 (d) ₹81
13. 13.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 9 days (d) 25 days
14. 14.If 2 kites cost ₹22, how much do 4 kites cost? (a) ₹88 (b) ₹24 (c) ₹55 (d) ₹44
15. 15.9 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 11 days (d) 6 days
16. 16.If 6 mangoes cost ₹132, how much do 5 mangoes cost? (a) ₹131 (b) ₹132 (c) ₹660 (d) ₹110
17. 17.If 2 mangoes cost ₹16, how much do 3 mangoes cost? (a) ₹17 (b) ₹48 (c) ₹32 (d) ₹24
18. 18.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 12 days (c) 19 days (d) 18 days
19. 19.8 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 24 days (c) 14 days (d) 25 days
20. 20.₹245 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹196 (b) ₹98 (c) ₹49 (d) ₹147
21. 21.If 6 notebooks cost ₹96, how much do 3 notebooks cost? (a) ₹48 (b) ₹64 (c) ₹288 (d) ₹93
22. 22.4 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) 10 days (d) 4 days
23. 23.₹294 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹105 (b) ₹147 (c) ₹21 (d) ₹189
24. 24.If 6 pens cost ₹108, how much do 5 pens cost? (a) ₹540 (b) ₹107 (c) ₹108 (d) ₹90
25. 25.₹198 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹108 (b) ₹99 (c) ₹18 (d) ₹90
26. 26.If 4 pens cost ₹12, how much do 5 pens cost? (a) ₹15 (b) ₹18 (c) ₹13 (d) ₹60
27. 27.If 4 mangoes cost ₹72, how much do 7 mangoes cost? (a) ₹504 (b) ₹75 (c) ₹144 (d) ₹126
28. 28.₹147 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹105 (b) ₹126 (c) ₹42 (d) ₹21
29. 29.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 16 days (c) 11 days (d) 15 days
30. 30.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹7 (b) ₹49 (c) ₹42 (d) ₹35
31. 31.If 2 notebooks cost ₹10, how much do 7 notebooks cost? (a) ₹70 (b) ₹15 (c) ₹40 (d) ₹35
32. 32.If 4 mangoes cost ₹12, how much do 5 mangoes cost? (a) ₹13 (b) ₹60 (c) ₹18 (d) ₹15
33. 33.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 39 days (c) 19 days (d) 7 days
34. 34.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 8 days (c) 57 days (d) 56 days
35. 35.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 13 days (c) 15 days (d) 9 days
36. 36.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 13 days (d) 11 days
37. 37.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 17 days (b) 2 days (c) 3 days (d) 4 days
38. 38.₹288 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹168 (b) ₹120 (c) ₹24 (d) ₹144
39. 39.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 25 days (d) 24 days
40. 40.If 9 pens cost ₹117, how much do 3 pens cost? (a) ₹351 (b) ₹111 (c) ₹39 (d) ₹52

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