Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 861 · 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 8 notebooks cost ₹152, how much do 2 notebooks cost? (a) ₹57 (b) ₹38 (c) ₹304 (d) ₹146
2. 2.If 9 mangoes cost ₹180, how much do 7 mangoes cost? (a) ₹140 (b) ₹160 (c) ₹178 (d) ₹1260
3. 3.If 5 kites cost ₹110, how much do 8 kites cost? (a) ₹113 (b) ₹198 (c) ₹176 (d) ₹880
4. 4.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 11 days (d) 9 days
5. 5.₹170 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹102 (b) ₹68 (c) ₹85 (d) ₹34
6. 6.If 2 kites cost ₹34, how much do 6 kites cost? (a) ₹119 (b) ₹204 (c) ₹38 (d) ₹102
7. 7.₹310 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹155 (b) ₹31 (c) ₹310 (d) ₹279
8. 8.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 32 days (b) 33 days (c) 2 days (d) 14 days
9. 9.₹517 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹282 (b) ₹235 (c) ₹329 (d) ₹47
10. 10.If 7 pens cost ₹28, how much do 3 pens cost? (a) ₹84 (b) ₹16 (c) ₹24 (d) ₹12
11. 11.If 4 notebooks cost ₹56, how much do 9 notebooks cost? (a) ₹61 (b) ₹504 (c) ₹126 (d) ₹140
12. 12.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 1 day (c) 16 days (d) 9 days
13. 13.₹48 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹24 (b) ₹40 (c) ₹48 (d) ₹8
14. 14.If 8 pens cost ₹56, how much do 9 pens cost? (a) ₹57 (b) ₹504 (c) ₹63 (d) ₹70
15. 15.If 6 mangoes cost ₹108, how much do 7 mangoes cost? (a) ₹756 (b) ₹144 (c) ₹109 (d) ₹126
16. 16.₹126 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹45 (b) ₹63 (c) ₹81 (d) ₹9
17. 17.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 17 days (d) 16 days
18. 18.₹57 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹19 (b) ₹57 (c) ₹39 (d) ₹38
19. 19.₹225 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹150 (b) ₹25 (c) ₹125 (d) ₹100
20. 20.If 7 mangoes cost ₹140, how much do 3 mangoes cost? (a) ₹136 (b) ₹80 (c) ₹420 (d) ₹60
21. 21.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 5 days (d) 6 days
22. 22.If 4 kites cost ₹36, how much do 12 kites cost? (a) ₹44 (b) ₹108 (c) ₹432 (d) ₹117
23. 23.If 3 mangoes cost ₹63, how much do 4 mangoes cost? (a) ₹64 (b) ₹84 (c) ₹252 (d) ₹105
24. 24.If 2 kites cost ₹26, how much do 3 kites cost? (a) ₹27 (b) ₹52 (c) ₹39 (d) ₹78
25. 25.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 6 days (d) 8 days
26. 26.₹72 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹48 (b) ₹24 (c) ₹36 (d) ₹72
27. 27.If 2 notebooks cost ₹40, how much do 3 notebooks cost? (a) ₹60 (b) ₹80 (c) ₹41 (d) ₹120
28. 28.If 3 mangoes cost ₹42, how much do 9 mangoes cost? (a) ₹48 (b) ₹140 (c) ₹378 (d) ₹126
29. 29.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 15 days (b) 20 days (c) 6 days (d) 5 days
30. 30.₹528 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹264 (b) ₹96 (c) ₹432 (d) ₹48
31. 31.₹495 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹450 (b) ₹45 (c) ₹90 (d) ₹405
32. 32.₹50 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹25 (b) ₹5 (c) ₹50 (d) ₹45
33. 33.If 2 mangoes cost ₹14, how much do 4 mangoes cost? (a) ₹35 (b) ₹16 (c) ₹28 (d) ₹56
34. 34.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹102 (b) ₹17 (c) ₹119 (d) ₹85
35. 35.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 12 days (c) 6 days (d) 7 days
36. 36.₹616 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹396 (b) ₹220 (c) ₹44 (d) ₹308
37. 37.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 26 days (c) 27 days (d) 16 days
38. 38.If 6 kites cost ₹96, how much do 10 kites cost? (a) ₹960 (b) ₹160 (c) ₹176 (d) ₹100
39. 39.If 4 pens cost ₹16, how much do 8 pens cost? (a) ₹36 (b) ₹128 (c) ₹32 (d) ₹20
40. 40.₹152 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹76 (b) ₹152 (c) ₹38 (d) ₹114

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