Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 460 · 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 4 pens cost ₹76, how much do 5 pens cost? (a) ₹77 (b) ₹95 (c) ₹380 (d) ₹114
2. 2.If 4 notebooks cost ₹24, how much do 8 notebooks cost? (a) ₹192 (b) ₹48 (c) ₹28 (d) ₹54
3. 3.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 12 days (d) 5 days
4. 4.If 7 pens cost ₹77, how much do 2 pens cost? (a) ₹154 (b) ₹72 (c) ₹33 (d) ₹22
5. 5.If 2 kites cost ₹18, how much do 3 kites cost? (a) ₹36 (b) ₹54 (c) ₹19 (d) ₹27
6. 6.If 2 pens cost ₹22, how much do 4 pens cost? (a) ₹44 (b) ₹24 (c) ₹55 (d) ₹88
7. 7.If 6 kites cost ₹90, how much do 2 kites cost? (a) ₹180 (b) ₹86 (c) ₹45 (d) ₹30
8. 8.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 17 days (d) 9 days
9. 9.If 8 notebooks cost ₹96, how much do 9 notebooks cost? (a) ₹97 (b) ₹108 (c) ₹864 (d) ₹120
10. 10.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 6 days (d) 24 days
11. 11.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 5 days (d) 7 days
12. 12.If 5 notebooks cost ₹65, how much do 4 notebooks cost? (a) ₹52 (b) ₹260 (c) ₹65 (d) ₹64
13. 13.If 7 pens cost ₹56, how much do 12 pens cost? (a) ₹61 (b) ₹672 (c) ₹104 (d) ₹96
14. 14.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 11 days (c) 17 days (d) 36 days
15. 15.₹350 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹175 (b) ₹50 (c) ₹200 (d) ₹150
16. 16.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 7 days (d) 4 days
17. 17.₹376 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹188 (b) ₹141 (c) ₹235 (d) ₹47
18. 18.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 16 days (d) 15 days
19. 19.If 8 notebooks cost ₹160, how much do 9 notebooks cost? (a) ₹200 (b) ₹161 (c) ₹1440 (d) ₹180
20. 20.₹154 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹14 (b) ₹56 (c) ₹77 (d) ₹98
21. 21.₹546 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹42 (b) ₹273 (c) ₹336 (d) ₹210
22. 22.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 17 days (c) 39 days (d) 9 days
23. 23.If 2 mangoes cost ₹46, how much do 4 mangoes cost? (a) ₹184 (b) ₹48 (c) ₹92 (d) ₹115
24. 24.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 7 days (d) 9 days
25. 25.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 4 days (d) 6 days
26. 26.If 2 mangoes cost ₹16, how much do 7 mangoes cost? (a) ₹64 (b) ₹56 (c) ₹112 (d) ₹21
27. 27.₹400 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹150 (b) ₹200 (c) ₹50 (d) ₹250
28. 28.If 8 kites cost ₹48, how much do 4 kites cost? (a) ₹24 (b) ₹30 (c) ₹192 (d) ₹44
29. 29.If 7 pens cost ₹77, how much do 8 pens cost? (a) ₹616 (b) ₹88 (c) ₹78 (d) ₹99
30. 30.₹240 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹90 (b) ₹120 (c) ₹30 (d) ₹150
31. 31.If 4 mangoes cost ₹100, how much do 5 mangoes cost? (a) ₹500 (b) ₹101 (c) ₹125 (d) ₹150
32. 32.If 8 pens cost ₹56, how much do 12 pens cost? (a) ₹672 (b) ₹60 (c) ₹91 (d) ₹84
33. 33.If 8 notebooks cost ₹120, how much do 10 notebooks cost? (a) ₹122 (b) ₹150 (c) ₹1200 (d) ₹165
34. 34.₹81 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹36 (b) ₹54 (c) ₹45 (d) ₹9
35. 35.₹85 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹68 (b) ₹17 (c) ₹34 (d) ₹51
36. 36.If 2 kites cost ₹26, how much do 10 kites cost? (a) ₹34 (b) ₹130 (c) ₹143 (d) ₹260
37. 37.If 7 notebooks cost ₹161, how much do 8 notebooks cost? (a) ₹184 (b) ₹1288 (c) ₹207 (d) ₹162
38. 38.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 6 days (d) 7 days
39. 39.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 14 days (c) 15 days (d) 5 days
40. 40.If 5 notebooks cost ₹40, how much do 6 notebooks cost? (a) ₹56 (b) ₹48 (c) ₹240 (d) ₹41

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