Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 617 · 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 2 kites cost ₹26, how much do 8 kites cost? (a) ₹32 (b) ₹104 (c) ₹117 (d) ₹208
2. 2.If 6 pens cost ₹108, how much do 10 pens cost? (a) ₹198 (b) ₹1080 (c) ₹180 (d) ₹112
3. 3.If 2 kites cost ₹22, how much do 3 kites cost? (a) ₹44 (b) ₹66 (c) ₹23 (d) ₹33
4. 4.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 3 days (d) 10 days
5. 5.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 4 days (c) 10 days (d) 9 days
6. 6.If 3 pens cost ₹18, how much do 4 pens cost? (a) ₹24 (b) ₹30 (c) ₹19 (d) ₹72
7. 7.If 6 notebooks cost ₹42, how much do 7 notebooks cost? (a) ₹294 (b) ₹56 (c) ₹43 (d) ₹49
8. 8.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 9 days (d) 1 day
9. 9.If 2 pens cost ₹32, how much do 11 pens cost? (a) ₹352 (b) ₹176 (c) ₹192 (d) ₹41
10. 10.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 28 days (b) 17 days (c) 11 days (d) 7 days
11. 11.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 13 days
12. 12.₹490 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹315 (b) ₹175 (c) ₹245 (d) ₹35
13. 13.₹176 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹88 (b) ₹144 (c) ₹32 (d) ₹16
14. 14.If 4 notebooks cost ₹20, how much do 5 notebooks cost? (a) ₹100 (b) ₹21 (c) ₹25 (d) ₹30
15. 15.₹256 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹128 (b) ₹32 (c) ₹224 (d) ₹256
16. 16.If 8 pens cost ₹48, how much do 4 pens cost? (a) ₹44 (b) ₹24 (c) ₹30 (d) ₹192
17. 17.₹364 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹234 (b) ₹26 (c) ₹182 (d) ₹130
18. 18.If 8 pens cost ₹144, how much do 7 pens cost? (a) ₹143 (b) ₹144 (c) ₹126 (d) ₹1008
19. 19.₹143 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹26 (b) ₹13 (c) ₹130 (d) ₹117
20. 20.If 8 kites cost ₹200, how much do 11 kites cost? (a) ₹203 (b) ₹275 (c) ₹300 (d) ₹2200
21. 21.8 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 24 days (c) 18 days (d) 25 days
22. 22.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 12 days (c) 16 days (d) 7 days
23. 23.₹264 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹132 (b) ₹99 (c) ₹165 (d) ₹33
24. 24.If 9 pens cost ₹144, how much do 12 pens cost? (a) ₹192 (b) ₹147 (c) ₹208 (d) ₹1728
25. 25.If 7 mangoes cost ₹140, how much do 4 mangoes cost? (a) ₹100 (b) ₹137 (c) ₹80 (d) ₹560
26. 26.₹55 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹20 (b) ₹40 (c) ₹35 (d) ₹5
27. 27.₹110 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹90 (b) ₹55 (c) ₹20 (d) ₹10
28. 28.₹441 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹294 (b) ₹196 (c) ₹49 (d) ₹245
29. 29.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 14 days (b) 11 days (c) 15 days (d) 3 days
30. 30.If 4 pens cost ₹32, how much do 9 pens cost? (a) ₹288 (b) ₹80 (c) ₹72 (d) ₹37
31. 31.If 8 kites cost ₹152, how much do 9 kites cost? (a) ₹171 (b) ₹1368 (c) ₹153 (d) ₹190
32. 32.If 4 mangoes cost ₹72, how much do 9 mangoes cost? (a) ₹77 (b) ₹162 (c) ₹180 (d) ₹648
33. 33.If 9 mangoes cost ₹126, how much do 6 mangoes cost? (a) ₹756 (b) ₹123 (c) ₹98 (d) ₹84
34. 34.₹460 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹230 (b) ₹322 (c) ₹46 (d) ₹138
35. 35.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 24 days (b) 9 days (c) 6 days (d) 15 days
36. 36.If 5 kites cost ₹45, how much do 4 kites cost? (a) ₹45 (b) ₹180 (c) ₹44 (d) ₹36
37. 37.If 5 pens cost ₹120, how much do 3 pens cost? (a) ₹96 (b) ₹118 (c) ₹360 (d) ₹72
38. 38.₹55 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹55 (b) ₹11 (c) ₹44 (d) ₹45
39. 39.₹429 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹78 (b) ₹351 (c) ₹390 (d) ₹39
40. 40.If 3 mangoes cost ₹39, how much do 10 mangoes cost? (a) ₹390 (b) ₹143 (c) ₹130 (d) ₹46

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