Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 484 · 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 ₹68, how much do 5 pens cost? (a) ₹69 (b) ₹340 (c) ₹85 (d) ₹102
2. 2.If 4 pens cost ₹36, how much do 8 pens cost? (a) ₹81 (b) ₹288 (c) ₹40 (d) ₹72
3. 3.If 2 pens cost ₹46, how much do 8 pens cost? (a) ₹368 (b) ₹184 (c) ₹207 (d) ₹52
4. 4.If 5 mangoes cost ₹45, how much do 7 mangoes cost? (a) ₹47 (b) ₹72 (c) ₹63 (d) ₹315
5. 5.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 11 days
6. 6.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 16 days (d) 15 days
7. 7.₹297 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹264 (b) ₹66 (c) ₹33 (d) ₹231
8. 8.If 2 notebooks cost ₹38, how much do 4 notebooks cost? (a) ₹40 (b) ₹95 (c) ₹76 (d) ₹152
9. 9.₹45 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹15 (b) ₹30 (c) ₹31 (d) ₹45
10. 10.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 6 days (d) 5 days
11. 11.₹396 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹33 (b) ₹165 (c) ₹198 (d) ₹231
12. 12.₹550 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹50 (b) ₹400 (c) ₹150 (d) ₹275
13. 13.If 8 notebooks cost ₹200, how much do 12 notebooks cost? (a) ₹300 (b) ₹2400 (c) ₹204 (d) ₹325
14. 14.If 6 mangoes cost ₹126, how much do 7 mangoes cost? (a) ₹147 (b) ₹168 (c) ₹882 (d) ₹127
15. 15.If 8 notebooks cost ₹80, how much do 12 notebooks cost? (a) ₹960 (b) ₹84 (c) ₹120 (d) ₹130
16. 16.₹286 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹143 (b) ₹208 (c) ₹78 (d) ₹26
17. 17.If 2 pens cost ₹42, how much do 7 pens cost? (a) ₹168 (b) ₹47 (c) ₹294 (d) ₹147
18. 18.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 11 days (d) 9 days
19. 19.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 3 days (c) 2 days (d) 8 days
20. 20.If 4 mangoes cost ₹60, how much do 12 mangoes cost? (a) ₹720 (b) ₹195 (c) ₹68 (d) ₹180
21. 21.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 9 days
22. 22.If 9 pens cost ₹63, how much do 10 pens cost? (a) ₹70 (b) ₹64 (c) ₹630 (d) ₹77
23. 23.₹119 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹17 (b) ₹68 (c) ₹85 (d) ₹51
24. 24.If 6 notebooks cost ₹108, how much do 4 notebooks cost? (a) ₹72 (b) ₹432 (c) ₹90 (d) ₹106
25. 25.₹507 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹312 (b) ₹195 (c) ₹39 (d) ₹351
26. 26.₹175 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹150 (b) ₹50 (c) ₹25 (d) ₹125
27. 27.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 22 days (d) 23 days
28. 28.₹154 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹44 (b) ₹22 (c) ₹77 (d) ₹110
29. 29.If 2 mangoes cost ₹10, how much do 8 mangoes cost? (a) ₹16 (b) ₹80 (c) ₹40 (d) ₹45
30. 30.If 4 kites cost ₹96, how much do 12 kites cost? (a) ₹104 (b) ₹288 (c) ₹1152 (d) ₹312
31. 31.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 15 days (c) 2 days (d) 10 days
32. 32.If 6 kites cost ₹144, how much do 7 kites cost? (a) ₹192 (b) ₹145 (c) ₹168 (d) ₹1008
33. 33.If 9 notebooks cost ₹126, how much do 4 notebooks cost? (a) ₹504 (b) ₹56 (c) ₹70 (d) ₹121
34. 34.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 19 days (c) 9 days (d) 49 days
35. 35.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 11 days (d) 26 days
36. 36.If 7 pens cost ₹84, how much do 9 pens cost? (a) ₹120 (b) ₹86 (c) ₹756 (d) ₹108
37. 37.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 9 days (d) 7 days
38. 38.₹299 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹23 (b) ₹184 (c) ₹207 (d) ₹115
39. 39.₹30 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹10 (b) ₹15 (c) ₹20 (d) ₹30
40. 40.If 2 notebooks cost ₹10, how much do 9 notebooks cost? (a) ₹50 (b) ₹17 (c) ₹45 (d) ₹90

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