Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 814 · 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.₹184 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹92 (b) ₹184 (c) ₹138 (d) ₹46
2. 2.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 40 days (c) 7 days (d) 19 days
3. 3.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 3 days (d) 4 days
4. 4.If 6 notebooks cost ₹132, how much do 10 notebooks cost? (a) ₹1320 (b) ₹136 (c) ₹242 (d) ₹220
5. 5.₹414 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹184 (b) ₹46 (c) ₹207 (d) ₹230
6. 6.If 2 notebooks cost ₹22, how much do 5 notebooks cost? (a) ₹55 (b) ₹25 (c) ₹110 (d) ₹66
7. 7.If 8 mangoes cost ₹168, how much do 3 mangoes cost? (a) ₹504 (b) ₹84 (c) ₹163 (d) ₹63
8. 8.₹220 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹110 (b) ₹20 (c) ₹40 (d) ₹180
9. 9.₹506 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹253 (b) ₹230 (c) ₹46 (d) ₹276
10. 10.If 4 kites cost ₹40, how much do 9 kites cost? (a) ₹360 (b) ₹45 (c) ₹90 (d) ₹100
11. 11.If 7 mangoes cost ₹21, how much do 9 mangoes cost? (a) ₹189 (b) ₹23 (c) ₹27 (d) ₹30
12. 12.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 17 days (d) 6 days
13. 13.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 8 days (d) 9 days
14. 14.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 40 days (d) 41 days
15. 15.₹196 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹140 (b) ₹98 (c) ₹28 (d) ₹56
16. 16.₹210 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹84 (b) ₹105 (c) ₹42 (d) ₹126
17. 17.If 8 notebooks cost ₹80, how much do 6 notebooks cost? (a) ₹70 (b) ₹78 (c) ₹60 (d) ₹480
18. 18.If 7 mangoes cost ₹84, how much do 8 mangoes cost? (a) ₹672 (b) ₹85 (c) ₹96 (d) ₹108
19. 19.If 3 mangoes cost ₹24, how much do 8 mangoes cost? (a) ₹192 (b) ₹29 (c) ₹72 (d) ₹64
20. 20.If 4 notebooks cost ₹40, how much do 10 notebooks cost? (a) ₹46 (b) ₹400 (c) ₹110 (d) ₹100
21. 21.₹312 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹182 (b) ₹156 (c) ₹130 (d) ₹26
22. 22.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 10 days (d) 2 days
23. 23.₹540 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹270 (b) ₹45 (c) ₹225 (d) ₹315
24. 24.If 7 notebooks cost ₹56, how much do 9 notebooks cost? (a) ₹58 (b) ₹504 (c) ₹72 (d) ₹80
25. 25.If 8 mangoes cost ₹96, how much do 10 mangoes cost? (a) ₹120 (b) ₹132 (c) ₹960 (d) ₹98
26. 26.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 14 days (c) 15 days (d) 9 days
27. 27.₹45 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹30 (b) ₹5 (c) ₹25 (d) ₹20
28. 28.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 28 days (d) 7 days
29. 29.If 4 kites cost ₹96, how much do 3 kites cost? (a) ₹288 (b) ₹96 (c) ₹72 (d) ₹95
30. 30.If 5 pens cost ₹115, how much do 8 pens cost? (a) ₹184 (b) ₹920 (c) ₹118 (d) ₹207
31. 31.If 2 mangoes cost ₹8, how much do 6 mangoes cost? (a) ₹12 (b) ₹24 (c) ₹48 (d) ₹28
32. 32.₹85 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹85 (b) ₹68 (c) ₹17 (d) ₹69
33. 33.If 4 mangoes cost ₹68, how much do 11 mangoes cost? (a) ₹204 (b) ₹748 (c) ₹75 (d) ₹187
34. 34.₹138 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹69 (b) ₹138 (c) ₹23 (d) ₹115
35. 35.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 10 days (d) 15 days
36. 36.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 35 days (b) 36 days (c) 11 days (d) 19 days
37. 37.If 7 pens cost ₹175, how much do 3 pens cost? (a) ₹75 (b) ₹171 (c) ₹525 (d) ₹100
38. 38.₹360 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹180 (b) ₹200 (c) ₹40 (d) ₹160
39. 39.If 3 mangoes cost ₹27, how much do 2 mangoes cost? (a) ₹18 (b) ₹54 (c) ₹26 (d) ₹27
40. 40.If 9 notebooks cost ₹99, how much do 4 notebooks cost? (a) ₹396 (b) ₹55 (c) ₹94 (d) ₹44

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