Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 868 · 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 6 kites cost ₹30, how much do 12 kites cost? (a) ₹60 (b) ₹360 (c) ₹65 (d) ₹36
2. 2.If 6 mangoes cost ₹54, how much do 2 mangoes cost? (a) ₹27 (b) ₹108 (c) ₹18 (d) ₹50
3. 3.If 3 notebooks cost ₹36, how much do 4 notebooks cost? (a) ₹144 (b) ₹37 (c) ₹60 (d) ₹48
4. 4.If 2 kites cost ₹38, how much do 11 kites cost? (a) ₹228 (b) ₹209 (c) ₹47 (d) ₹418
5. 5.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 16 days (c) 5 days (d) 7 days
6. 6.₹414 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹207 (b) ₹184 (c) ₹46 (d) ₹230
7. 7.₹136 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹51 (b) ₹85 (c) ₹17 (d) ₹68
8. 8.₹132 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹55 (b) ₹66 (c) ₹11 (d) ₹77
9. 9.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 20 days (c) 8 days (d) 56 days
10. 10.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 1 day (d) 7 days
11. 11.5 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 19 days (d) 4 days
12. 12.₹396 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹220 (b) ₹198 (c) ₹176 (d) ₹44
13. 13.₹100 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹50 (b) ₹25 (c) ₹75 (d) ₹100
14. 14.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 31 days (b) 30 days (c) 16 days (d) 4 days
15. 15.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 14 days (c) 23 days (d) 8 days
16. 16.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 17 days (c) 4 days (d) 6 days
17. 17.₹117 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹65 (b) ₹13 (c) ₹52 (d) ₹78
18. 18.If 4 kites cost ₹36, how much do 12 kites cost? (a) ₹44 (b) ₹432 (c) ₹108 (d) ₹117
19. 19.₹50 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹25 (b) ₹50 (c) ₹40 (d) ₹10
20. 20.If 2 mangoes cost ₹24, how much do 7 mangoes cost? (a) ₹168 (b) ₹29 (c) ₹96 (d) ₹84
21. 21.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 2 days (d) 11 days
22. 22.₹126 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹45 (b) ₹63 (c) ₹81 (d) ₹9
23. 23.If 4 mangoes cost ₹28, how much do 12 mangoes cost? (a) ₹36 (b) ₹84 (c) ₹336 (d) ₹91
24. 24.₹95 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹76 (b) ₹19 (c) ₹38 (d) ₹57
25. 25.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 32 days (b) 14 days (c) 33 days (d) 2 days
26. 26.If 6 notebooks cost ₹18, how much do 7 notebooks cost? (a) ₹126 (b) ₹24 (c) ₹21 (d) ₹19
27. 27.If 3 kites cost ₹24, how much do 11 kites cost? (a) ₹32 (b) ₹88 (c) ₹96 (d) ₹264
28. 28.If 2 kites cost ₹10, how much do 8 kites cost? (a) ₹16 (b) ₹80 (c) ₹40 (d) ₹45
29. 29.If 8 mangoes cost ₹64, how much do 2 mangoes cost? (a) ₹16 (b) ₹24 (c) ₹58 (d) ₹128
30. 30.₹112 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹32 (b) ₹16 (c) ₹56 (d) ₹80
31. 31.If 3 notebooks cost ₹39, how much do 7 notebooks cost? (a) ₹43 (b) ₹273 (c) ₹91 (d) ₹104
32. 32.If 2 mangoes cost ₹28, how much do 9 mangoes cost? (a) ₹126 (b) ₹35 (c) ₹252 (d) ₹140
33. 33.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 11 days (d) 9 days
34. 34.₹120 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹108 (b) ₹12 (c) ₹60 (d) ₹120
35. 35.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 3 days (d) 1 day
36. 36.If 8 kites cost ₹168, how much do 9 kites cost? (a) ₹169 (b) ₹1512 (c) ₹189 (d) ₹210
37. 37.If 9 pens cost ₹108, how much do 8 pens cost? (a) ₹864 (b) ₹108 (c) ₹96 (d) ₹107
38. 38.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 19 days (c) 4 days (d) 49 days
39. 39.8 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 8 days (c) 6 days (d) 24 days
40. 40.₹210 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹210 (b) ₹35 (c) ₹175 (d) ₹105

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