Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 120 · 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 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 49 days (d) 19 days
2. 2.₹147 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹21 (b) ₹105 (c) ₹126 (d) ₹42
3. 3.If 6 notebooks cost ₹42, how much do 7 notebooks cost? (a) ₹49 (b) ₹294 (c) ₹56 (d) ₹43
4. 4.₹120 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹60 (b) ₹84 (c) ₹36 (d) ₹12
5. 5.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 28 days (c) 7 days (d) 16 days
6. 6.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 7 days (d) 8 days
7. 7.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 7 days (d) 2 days
8. 8.If 8 mangoes cost ₹168, how much do 12 mangoes cost? (a) ₹273 (b) ₹2016 (c) ₹252 (d) ₹172
9. 9.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 24 days (c) 16 days (d) 6 days
10. 10.₹91 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹91 (b) ₹13 (c) ₹78 (d) ₹79
11. 11.If 9 kites cost ₹135, how much do 7 kites cost? (a) ₹133 (b) ₹105 (c) ₹120 (d) ₹945
12. 12.If 7 notebooks cost ₹91, how much do 8 notebooks cost? (a) ₹117 (b) ₹104 (c) ₹728 (d) ₹92
13. 13.8 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 13 days (c) 7 days (d) 6 days
14. 14.₹132 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹108 (b) ₹12 (c) ₹66 (d) ₹24
15. 15.If 7 mangoes cost ₹42, how much do 12 mangoes cost? (a) ₹47 (b) ₹78 (c) ₹504 (d) ₹72
16. 16.₹76 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹38 (b) ₹76 (c) ₹57 (d) ₹19
17. 17.₹80 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹40 (b) ₹24 (c) ₹56 (d) ₹8
18. 18.₹176 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹112 (b) ₹16 (c) ₹88 (d) ₹64
19. 19.₹104 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹13 (b) ₹104 (c) ₹52 (d) ₹91
20. 20.7 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
21. 21.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 3 days (d) 9 days
22. 22.If 6 kites cost ₹126, how much do 4 kites cost? (a) ₹504 (b) ₹124 (c) ₹84 (d) ₹105
23. 23.If 2 mangoes cost ₹16, how much do 12 mangoes cost? (a) ₹26 (b) ₹192 (c) ₹104 (d) ₹96
24. 24.3 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
25. 25.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 19 days (d) 4 days
26. 26.If 2 pens cost ₹42, how much do 7 pens cost? (a) ₹168 (b) ₹147 (c) ₹47 (d) ₹294
27. 27.If 3 notebooks cost ₹9, how much do 9 notebooks cost? (a) ₹30 (b) ₹15 (c) ₹27 (d) ₹81
28. 28.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 15 days (c) 11 days (d) 14 days
29. 29.₹150 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹150 (b) ₹120 (c) ₹75 (d) ₹30
30. 30.If 3 mangoes cost ₹12, how much do 4 mangoes cost? (a) ₹20 (b) ₹16 (c) ₹13 (d) ₹48
31. 31.If 3 notebooks cost ₹30, how much do 10 notebooks cost? (a) ₹37 (b) ₹300 (c) ₹100 (d) ₹110
32. 32.If 8 mangoes cost ₹64, how much do 4 mangoes cost? (a) ₹60 (b) ₹40 (c) ₹32 (d) ₹256
33. 33.If 7 kites cost ₹133, how much do 4 kites cost? (a) ₹95 (b) ₹130 (c) ₹532 (d) ₹76
34. 34.If 7 pens cost ₹133, how much do 8 pens cost? (a) ₹134 (b) ₹152 (c) ₹1064 (d) ₹171
35. 35.₹110 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹55 (b) ₹44 (c) ₹66 (d) ₹22
36. 36.If 7 notebooks cost ₹154, how much do 9 notebooks cost? (a) ₹220 (b) ₹1386 (c) ₹198 (d) ₹156
37. 37.If 5 pens cost ₹40, how much do 11 pens cost? (a) ₹440 (b) ₹46 (c) ₹96 (d) ₹88
38. 38.If 3 pens cost ₹18, how much do 5 pens cost? (a) ₹36 (b) ₹30 (c) ₹90 (d) ₹20
39. 39.If 8 notebooks cost ₹32, how much do 5 notebooks cost? (a) ₹29 (b) ₹24 (c) ₹160 (d) ₹20
40. 40.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 2 days (c) 6 days (d) 7 days

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