Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 308 · 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.₹175 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹35 (b) ₹141 (c) ₹140 (d) ₹175
2. 2.₹84 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹7 (b) ₹35 (c) ₹42 (d) ₹49
3. 3.₹403 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹155 (b) ₹279 (c) ₹248 (d) ₹31
4. 4.₹105 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹60 (b) ₹75 (c) ₹45 (d) ₹15
5. 5.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 16 days (c) 28 days (d) 29 days
6. 6.If 2 mangoes cost ₹6, how much do 9 mangoes cost? (a) ₹27 (b) ₹54 (c) ₹13 (d) ₹30
7. 7.If 2 mangoes cost ₹34, how much do 4 mangoes cost? (a) ₹136 (b) ₹68 (c) ₹85 (d) ₹36
8. 8.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 36 days (c) 35 days (d) 19 days
9. 9.If 5 notebooks cost ₹75, how much do 6 notebooks cost? (a) ₹76 (b) ₹450 (c) ₹90 (d) ₹105
10. 10.If 6 mangoes cost ₹36, how much do 2 mangoes cost? (a) ₹12 (b) ₹72 (c) ₹18 (d) ₹32
11. 11.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 53 days (c) 7 days (d) 52 days
12. 12.4 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 18 days (b) 14 days (c) 8 days (d) 10 days
13. 13.If 6 pens cost ₹114, how much do 3 pens cost? (a) ₹57 (b) ₹111 (c) ₹76 (d) ₹342
14. 14.If 5 kites cost ₹95, how much do 3 kites cost? (a) ₹76 (b) ₹57 (c) ₹285 (d) ₹93
15. 15.If 8 mangoes cost ₹136, how much do 5 mangoes cost? (a) ₹680 (b) ₹102 (c) ₹85 (d) ₹133
16. 16.If 3 notebooks cost ₹9, how much do 9 notebooks cost? (a) ₹15 (b) ₹30 (c) ₹81 (d) ₹27
17. 17.₹184 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹115 (b) ₹69 (c) ₹23 (d) ₹92
18. 18.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 13 days (c) 9 days (d) 23 days
19. 19.If 6 kites cost ₹150, how much do 8 kites cost? (a) ₹152 (b) ₹200 (c) ₹225 (d) ₹1200
20. 20.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 2 days (d) 8 days
21. 21.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 25 days (d) 13 days
22. 22.If 3 pens cost ₹18, how much do 8 pens cost? (a) ₹23 (b) ₹144 (c) ₹48 (d) ₹54
23. 23.If 4 kites cost ₹64, how much do 3 kites cost? (a) ₹63 (b) ₹192 (c) ₹64 (d) ₹48
24. 24.₹99 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹67 (b) ₹99 (c) ₹66 (d) ₹33
25. 25.If 5 mangoes cost ₹80, how much do 6 mangoes cost? (a) ₹81 (b) ₹96 (c) ₹480 (d) ₹112
26. 26.₹330 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹270 (b) ₹30 (c) ₹165 (d) ₹60
27. 27.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 19 days (c) 2 days (d) 3 days
28. 28.₹658 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹235 (b) ₹329 (c) ₹423 (d) ₹47
29. 29.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 3 days (d) 4 days
30. 30.₹203 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹29 (b) ₹58 (c) ₹174 (d) ₹145
31. 31.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 30 days (b) 4 days (c) 31 days (d) 16 days
32. 32.₹160 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹20 (b) ₹80 (c) ₹160 (d) ₹140
33. 33.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 45 days (c) 5 days (d) 44 days
34. 34.₹462 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹210 (b) ₹252 (c) ₹231 (d) ₹42
35. 35.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 17 days (d) 5 days
36. 36.₹481 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹370 (b) ₹37 (c) ₹333 (d) ₹148
37. 37.If 9 mangoes cost ₹99, how much do 6 mangoes cost? (a) ₹96 (b) ₹66 (c) ₹77 (d) ₹594
38. 38.₹64 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹32 (b) ₹48 (c) ₹16 (d) ₹64
39. 39.If 4 notebooks cost ₹12, how much do 6 notebooks cost? (a) ₹18 (b) ₹14 (c) ₹21 (d) ₹72
40. 40.₹182 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹91 (b) ₹13 (c) ₹117 (d) ₹65

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