Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 12 · 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 6 mangoes cost ₹120, how much do 3 mangoes cost? (a) ₹60 (b) ₹80 (c) ₹117 (d) ₹360
2. 2.₹312 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹156 (b) ₹24 (c) ₹192 (d) ₹120
3. 3.₹468 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹234 (b) ₹288 (c) ₹180 (d) ₹36
4. 4.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 4 days (d) 6 days
5. 5.If 5 notebooks cost ₹30, how much do 3 notebooks cost? (a) ₹18 (b) ₹28 (c) ₹24 (d) ₹90
6. 6.If 6 notebooks cost ₹84, how much do 7 notebooks cost? (a) ₹588 (b) ₹112 (c) ₹85 (d) ₹98
7. 7.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 30 days (c) 31 days (d) 19 days
8. 8.If 6 notebooks cost ₹48, how much do 11 notebooks cost? (a) ₹53 (b) ₹528 (c) ₹96 (d) ₹88
9. 9.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 11 days (d) 9 days
10. 10.₹210 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹135 (b) ₹75 (c) ₹105 (d) ₹15
11. 11.If 8 mangoes cost ₹80, how much do 10 mangoes cost? (a) ₹110 (b) ₹800 (c) ₹100 (d) ₹82
12. 12.If 6 kites cost ₹138, how much do 2 kites cost? (a) ₹46 (b) ₹69 (c) ₹276 (d) ₹134
13. 13.If 8 kites cost ₹56, how much do 9 kites cost? (a) ₹63 (b) ₹70 (c) ₹504 (d) ₹57
14. 14.₹117 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹36 (b) ₹9 (c) ₹81 (d) ₹90
15. 15.If 2 notebooks cost ₹46, how much do 3 notebooks cost? (a) ₹138 (b) ₹47 (c) ₹92 (d) ₹69
16. 16.If 7 mangoes cost ₹42, how much do 8 mangoes cost? (a) ₹48 (b) ₹336 (c) ₹54 (d) ₹43
17. 17.If 8 pens cost ₹24, how much do 3 pens cost? (a) ₹12 (b) ₹72 (c) ₹9 (d) ₹19
18. 18.₹448 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹288 (b) ₹160 (c) ₹224 (d) ₹32
19. 19.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 19 days (d) 4 days
20. 20.If 4 pens cost ₹12, how much do 6 pens cost? (a) ₹72 (b) ₹14 (c) ₹21 (d) ₹18
21. 21.If 7 mangoes cost ₹175, how much do 6 mangoes cost? (a) ₹150 (b) ₹174 (c) ₹175 (d) ₹1050
22. 22.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 21 days (d) 22 days
23. 23.₹78 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹78 (b) ₹52 (c) ₹26 (d) ₹39
24. 24.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 2 days (d) 7 days
25. 25.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 7 days (d) 20 days
26. 26.₹588 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹245 (b) ₹343 (c) ₹49 (d) ₹294
27. 27.₹208 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹26 (b) ₹78 (c) ₹130 (d) ₹104
28. 28.₹315 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹45 (b) ₹225 (c) ₹180 (d) ₹135
29. 29.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 17 days (c) 13 days (d) 16 days
30. 30.If 2 kites cost ₹20, how much do 9 kites cost? (a) ₹27 (b) ₹90 (c) ₹100 (d) ₹180
31. 31.₹88 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹44 (b) ₹64 (c) ₹8 (d) ₹24
32. 32.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 11 days (c) 15 days (d) 14 days
33. 33.₹120 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹30 (b) ₹120 (c) ₹60 (d) ₹90
34. 34.₹54 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹18 (b) ₹36 (c) ₹27 (d) ₹54
35. 35.₹310 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹93 (b) ₹155 (c) ₹31 (d) ₹217
36. 36.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 8 days (d) 7 days
37. 37.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 14 days (b) 18 days (c) 3 days (d) 2 days
38. 38.If 7 pens cost ₹70, how much do 6 pens cost? (a) ₹60 (b) ₹420 (c) ₹70 (d) ₹69
39. 39.₹50 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹10 (c) ₹30 (d) ₹25
40. 40.If 2 mangoes cost ₹14, how much do 3 mangoes cost? (a) ₹15 (b) ₹42 (c) ₹21 (d) ₹28

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