Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 472 · 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. 1.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 35 days (b) 19 days (c) 36 days (d) 11 days
2. 2.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 3 days (c) 4 days (d) 10 days
3. 3.If 3 mangoes cost ₹57, how much do 10 mangoes cost? (a) ₹570 (b) ₹190 (c) ₹209 (d) ₹64
4. 4.₹243 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹27 (b) ₹108 (c) ₹162 (d) ₹135
5. 5.If 8 notebooks cost ₹40, how much do 12 notebooks cost? (a) ₹44 (b) ₹60 (c) ₹65 (d) ₹480
6. 6.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 6 days (d) 9 days
7. 7.If 5 notebooks cost ₹35, how much do 11 notebooks cost? (a) ₹84 (b) ₹385 (c) ₹41 (d) ₹77
8. 8.If 2 pens cost ₹30, how much do 7 pens cost? (a) ₹35 (b) ₹120 (c) ₹210 (d) ₹105
9. 9.If 3 pens cost ₹48, how much do 6 pens cost? (a) ₹112 (b) ₹288 (c) ₹96 (d) ₹51
10. 10.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 16 days (d) 25 days
11. 11.If 7 notebooks cost ₹105, how much do 4 notebooks cost? (a) ₹60 (b) ₹75 (c) ₹420 (d) ₹102
12. 12.If 7 mangoes cost ₹77, how much do 8 mangoes cost? (a) ₹78 (b) ₹88 (c) ₹616 (d) ₹99
13. 13.₹110 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹40 (b) ₹70 (c) ₹10 (d) ₹55
14. 14.₹376 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹47 (b) ₹235 (c) ₹188 (d) ₹141
15. 15.₹330 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹165 (b) ₹30 (c) ₹60 (d) ₹270
16. 16.If 4 kites cost ₹12, how much do 2 kites cost? (a) ₹10 (b) ₹9 (c) ₹24 (d) ₹6
17. 17.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 9 days (d) 45 days
18. 18.₹35 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹35 (b) ₹7 (c) ₹29 (d) ₹28
19. 19.If 7 pens cost ₹119, how much do 2 pens cost? (a) ₹51 (b) ₹238 (c) ₹34 (d) ₹114
20. 20.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 7 days (d) 8 days
21. 21.If 3 pens cost ₹57, how much do 7 pens cost? (a) ₹152 (b) ₹61 (c) ₹133 (d) ₹399
22. 22.If 7 kites cost ₹42, how much do 5 kites cost? (a) ₹210 (b) ₹40 (c) ₹36 (d) ₹30
23. 23.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 12 days (c) 2 days (d) 3 days
24. 24.If 6 notebooks cost ₹54, how much do 3 notebooks cost? (a) ₹36 (b) ₹51 (c) ₹162 (d) ₹27
25. 25.6 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 16 days (d) 4 days
26. 26.If 4 kites cost ₹56, how much do 12 kites cost? (a) ₹64 (b) ₹672 (c) ₹182 (d) ₹168
27. 27.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 9 days (d) 5 days
28. 28.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 3 days
29. 29.If 5 mangoes cost ₹65, how much do 11 mangoes cost? (a) ₹71 (b) ₹143 (c) ₹715 (d) ₹156
30. 30.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 5 days (c) 4 days (d) 3 days
31. 31.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 2 days (c) 3 days (d) 8 days
32. 32.If 2 kites cost ₹8, how much do 3 kites cost? (a) ₹24 (b) ₹9 (c) ₹16 (d) ₹12
33. 33.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 27 days (c) 26 days (d) 9 days
34. 34.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 8 days (d) 13 days
35. 35.If 3 mangoes cost ₹21, how much do 10 mangoes cost? (a) ₹28 (b) ₹70 (c) ₹210 (d) ₹77
36. 36.If 9 mangoes cost ₹225, how much do 4 mangoes cost? (a) ₹220 (b) ₹125 (c) ₹900 (d) ₹100
37. 37.₹144 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹72 (b) ₹36 (c) ₹144 (d) ₹108
38. 38.If 7 notebooks cost ₹105, how much do 2 notebooks cost? (a) ₹30 (b) ₹100 (c) ₹210 (d) ₹45
39. 39.₹70 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹21 (b) ₹35 (c) ₹7 (d) ₹49
40. 40.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 5 days (c) 21 days (d) 13 days

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