Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 650 · 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 5 notebooks cost ₹60, how much do 6 notebooks cost? (a) ₹61 (b) ₹360 (c) ₹84 (d) ₹72
2. 2.If 7 kites cost ₹175, how much do 10 kites cost? (a) ₹275 (b) ₹178 (c) ₹250 (d) ₹1750
3. 3.If 7 kites cost ₹168, how much do 6 kites cost? (a) ₹1008 (b) ₹167 (c) ₹144 (d) ₹168
4. 4.If 3 mangoes cost ₹72, how much do 2 mangoes cost? (a) ₹144 (b) ₹71 (c) ₹48 (d) ₹72
5. 5.If 7 mangoes cost ₹175, how much do 2 mangoes cost? (a) ₹170 (b) ₹350 (c) ₹75 (d) ₹50
6. 6.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 11 days (c) 15 days (d) 16 days
7. 7.If 3 mangoes cost ₹18, how much do 4 mangoes cost? (a) ₹19 (b) ₹30 (c) ₹72 (d) ₹24
8. 8.₹288 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹288 (b) ₹48 (c) ₹240 (d) ₹144
9. 9.₹176 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹66 (b) ₹22 (c) ₹110 (d) ₹88
10. 10.₹168 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹84 (b) ₹120 (c) ₹48 (d) ₹24
11. 11.₹120 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹45 (b) ₹15 (c) ₹75 (d) ₹60
12. 12.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 17 days (d) 13 days
13. 13.₹50 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹40 (b) ₹10 (c) ₹50 (d) ₹25
14. 14.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 5 days (c) 4 days (d) 12 days
15. 15.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 13 days (c) 21 days (d) 22 days
16. 16.If 6 mangoes cost ₹102, how much do 8 mangoes cost? (a) ₹153 (b) ₹816 (c) ₹104 (d) ₹136
17. 17.If 4 mangoes cost ₹76, how much do 3 mangoes cost? (a) ₹57 (b) ₹228 (c) ₹76 (d) ₹75
18. 18.If 7 notebooks cost ₹147, how much do 3 notebooks cost? (a) ₹143 (b) ₹84 (c) ₹441 (d) ₹63
19. 19.If 4 notebooks cost ₹32, how much do 11 notebooks cost? (a) ₹88 (b) ₹96 (c) ₹39 (d) ₹352
20. 20.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 12 days (c) 28 days (d) 16 days
21. 21.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 15 days (c) 14 days (d) 10 days
22. 22.If 7 notebooks cost ₹42, how much do 10 notebooks cost? (a) ₹45 (b) ₹66 (c) ₹420 (d) ₹60
23. 23.If 6 kites cost ₹18, how much do 8 kites cost? (a) ₹20 (b) ₹144 (c) ₹27 (d) ₹24
24. 24.If 5 mangoes cost ₹110, how much do 6 mangoes cost? (a) ₹111 (b) ₹660 (c) ₹154 (d) ₹132
25. 25.If 9 kites cost ₹99, how much do 8 kites cost? (a) ₹88 (b) ₹99 (c) ₹98 (d) ₹792
26. 26.₹28 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹21 (b) ₹28 (c) ₹7 (d) ₹14
27. 27.₹387 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹258 (b) ₹172 (c) ₹215 (d) ₹43
28. 28.₹78 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹30 (b) ₹6 (c) ₹39 (d) ₹48
29. 29.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 13 days (d) 4 days
30. 30.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 4 days (d) 9 days
31. 31.If 3 notebooks cost ₹15, how much do 2 notebooks cost? (a) ₹14 (b) ₹30 (c) ₹15 (d) ₹10
32. 32.If 5 pens cost ₹40, how much do 10 pens cost? (a) ₹45 (b) ₹88 (c) ₹80 (d) ₹400
33. 33.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 4 days (d) 15 days
34. 34.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 14 days (b) 7 days (c) 9 days (d) 8 days
35. 35.If 8 kites cost ₹56, how much do 12 kites cost? (a) ₹60 (b) ₹91 (c) ₹84 (d) ₹672
36. 36.If 6 mangoes cost ₹72, how much do 7 mangoes cost? (a) ₹504 (b) ₹96 (c) ₹84 (d) ₹73
37. 37.₹352 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹44 (b) ₹176 (c) ₹132 (d) ₹220
38. 38.₹110 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹110 (b) ₹55 (c) ₹22 (d) ₹88
39. 39.If 2 pens cost ₹24, how much do 8 pens cost? (a) ₹30 (b) ₹108 (c) ₹96 (d) ₹192
40. 40.If 2 mangoes cost ₹14, how much do 12 mangoes cost? (a) ₹91 (b) ₹168 (c) ₹24 (d) ₹84

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