Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 210 · 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 7 pens cost ₹98, how much do 8 pens cost? (a) ₹99 (b) ₹112 (c) ₹784 (d) ₹126
2. 2.₹364 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹130 (b) ₹26 (c) ₹182 (d) ₹234
3. 3.₹333 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹37 (b) ₹296 (c) ₹297 (d) ₹333
4. 4.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 28 days (d) 11 days
5. 5.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 3 days
6. 6.If 6 mangoes cost ₹84, how much do 4 mangoes cost? (a) ₹56 (b) ₹336 (c) ₹70 (d) ₹82
7. 7.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 19 days (c) 39 days (d) 7 days
8. 8.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 2 days (d) 17 days
9. 9.₹124 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹31 (b) ₹124 (c) ₹62 (d) ₹93
10. 10.If 4 kites cost ₹76, how much do 2 kites cost? (a) ₹74 (b) ₹38 (c) ₹152 (d) ₹57
11. 11.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 13 days (d) 10 days
12. 12.If 8 pens cost ₹152, how much do 4 pens cost? (a) ₹95 (b) ₹148 (c) ₹76 (d) ₹608
13. 13.5 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
14. 14.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 27 days (c) 28 days (d) 13 days
15. 15.If 3 mangoes cost ₹69, how much do 9 mangoes cost? (a) ₹75 (b) ₹230 (c) ₹621 (d) ₹207
16. 16.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 21 days (d) 22 days
17. 17.If 4 kites cost ₹20, how much do 10 kites cost? (a) ₹55 (b) ₹26 (c) ₹50 (d) ₹200
18. 18.₹72 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹60 (b) ₹72 (c) ₹12 (d) ₹36
19. 19.If 8 notebooks cost ₹120, how much do 6 notebooks cost? (a) ₹105 (b) ₹118 (c) ₹90 (d) ₹720
20. 20.If 6 kites cost ₹78, how much do 11 kites cost? (a) ₹83 (b) ₹143 (c) ₹156 (d) ₹858
21. 21.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 32 days (b) 2 days (c) 3 days (d) 17 days
22. 22.If 8 notebooks cost ₹104, how much do 2 notebooks cost? (a) ₹208 (b) ₹98 (c) ₹26 (d) ₹39
23. 23.If 5 pens cost ₹40, how much do 7 pens cost? (a) ₹280 (b) ₹42 (c) ₹56 (d) ₹64
24. 24.If 5 mangoes cost ₹125, how much do 9 mangoes cost? (a) ₹250 (b) ₹1125 (c) ₹129 (d) ₹225
25. 25.If 3 mangoes cost ₹63, how much do 5 mangoes cost? (a) ₹65 (b) ₹315 (c) ₹126 (d) ₹105
26. 26.If 9 kites cost ₹153, how much do 5 kites cost? (a) ₹149 (b) ₹765 (c) ₹102 (d) ₹85
27. 27.If 7 mangoes cost ₹56, how much do 3 mangoes cost? (a) ₹168 (b) ₹52 (c) ₹32 (d) ₹24
28. 28.If 9 kites cost ₹36, how much do 10 kites cost? (a) ₹360 (b) ₹37 (c) ₹44 (d) ₹40
29. 29.If 6 kites cost ₹30, how much do 7 kites cost? (a) ₹210 (b) ₹31 (c) ₹40 (d) ₹35
30. 30.If 3 notebooks cost ₹15, how much do 12 notebooks cost? (a) ₹65 (b) ₹60 (c) ₹24 (d) ₹180
31. 31.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 9 days (c) 5 days (d) 15 days
32. 32.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 5 days (d) 4 days
33. 33.If 8 kites cost ₹152, how much do 3 kites cost? (a) ₹57 (b) ₹76 (c) ₹456 (d) ₹147
34. 34.If 6 mangoes cost ₹114, how much do 4 mangoes cost? (a) ₹112 (b) ₹95 (c) ₹456 (d) ₹76
35. 35.₹144 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹48 (b) ₹96 (c) ₹72 (d) ₹144
36. 36.If 3 notebooks cost ₹60, how much do 12 notebooks cost? (a) ₹69 (b) ₹260 (c) ₹720 (d) ₹240
37. 37.₹500 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹150 (b) ₹50 (c) ₹250 (d) ₹350
38. 38.₹55 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹40 (b) ₹5 (c) ₹35 (d) ₹20
39. 39.If 4 kites cost ₹60, how much do 10 kites cost? (a) ₹600 (b) ₹150 (c) ₹66 (d) ₹165
40. 40.₹300 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹25 (b) ₹175 (c) ₹125 (d) ₹150

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