Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 445 · 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.₹319 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹29 (b) ₹203 (c) ₹145 (d) ₹174
2. 2.If 3 notebooks cost ₹33, how much do 4 notebooks cost? (a) ₹34 (b) ₹55 (c) ₹44 (d) ₹132
3. 3.If 4 kites cost ₹80, how much do 10 kites cost? (a) ₹220 (b) ₹86 (c) ₹800 (d) ₹200
4. 4.₹110 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹66 (b) ₹55 (c) ₹44 (d) ₹22
5. 5.If 6 notebooks cost ₹132, how much do 3 notebooks cost? (a) ₹88 (b) ₹66 (c) ₹396 (d) ₹129
6. 6.₹260 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹260 (b) ₹130 (c) ₹26 (d) ₹234
7. 7.If 4 notebooks cost ₹36, how much do 2 notebooks cost? (a) ₹27 (b) ₹72 (c) ₹34 (d) ₹18
8. 8.If 2 mangoes cost ₹46, how much do 11 mangoes cost? (a) ₹276 (b) ₹253 (c) ₹55 (d) ₹506
9. 9.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 20 days (b) 4 days (c) 16 days (d) 5 days
10. 10.3 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 4 days (d) 11 days
11. 11.₹56 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹28 (b) ₹8 (c) ₹48 (d) ₹56
12. 12.If 4 mangoes cost ₹68, how much do 7 mangoes cost? (a) ₹136 (b) ₹71 (c) ₹119 (d) ₹476
13. 13.₹25 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹15 (b) ₹5 (c) ₹10 (d) ₹20
14. 14.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 9 days (d) 7 days
15. 15.₹287 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹164 (b) ₹123 (c) ₹205 (d) ₹41
16. 16.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 5 days (d) 4 days
17. 17.₹56 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹42 (b) ₹28 (c) ₹56 (d) ₹14
18. 18.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 14 days (b) 15 days (c) 11 days (d) 5 days
19. 19.₹121 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹88 (b) ₹11 (c) ₹44 (d) ₹77
20. 20.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 6 days (d) 18 days
21. 21.₹132 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹48 (b) ₹12 (c) ₹66 (d) ₹84
22. 22.If 6 pens cost ₹36, how much do 5 pens cost? (a) ₹30 (b) ₹180 (c) ₹36 (d) ₹35
23. 23.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 11 days (d) 4 days
24. 24.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 7 days (d) 8 days
25. 25.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 24 days (c) 8 days (d) 6 days
26. 26.If 6 notebooks cost ₹78, how much do 9 notebooks cost? (a) ₹81 (b) ₹117 (c) ₹702 (d) ₹130
27. 27.If 6 kites cost ₹18, how much do 7 kites cost? (a) ₹19 (b) ₹126 (c) ₹21 (d) ₹24
28. 28.If 7 pens cost ₹98, how much do 3 pens cost? (a) ₹56 (b) ₹94 (c) ₹294 (d) ₹42
29. 29.If 2 pens cost ₹24, how much do 9 pens cost? (a) ₹31 (b) ₹120 (c) ₹108 (d) ₹216
30. 30.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 15 days (c) 22 days (d) 13 days
31. 31.₹336 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹140 (b) ₹168 (c) ₹196 (d) ₹28
32. 32.If 2 mangoes cost ₹12, how much do 12 mangoes cost? (a) ₹22 (b) ₹144 (c) ₹72 (d) ₹78
33. 33.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 27 days (c) 7 days (d) 28 days
34. 34.If 5 notebooks cost ₹25, how much do 4 notebooks cost? (a) ₹20 (b) ₹100 (c) ₹24 (d) ₹25
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) 9 days (d) 15 days
36. 36.If 6 notebooks cost ₹138, how much do 7 notebooks cost? (a) ₹139 (b) ₹966 (c) ₹184 (d) ₹161
37. 37.₹156 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹65 (b) ₹78 (c) ₹91 (d) ₹13
38. 38.If 5 pens cost ₹55, how much do 11 pens cost? (a) ₹61 (b) ₹121 (c) ₹605 (d) ₹132
39. 39.₹351 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹39 (b) ₹312 (c) ₹78 (d) ₹273
40. 40.If 2 kites cost ₹30, how much do 10 kites cost? (a) ₹300 (b) ₹150 (c) ₹165 (d) ₹38

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