Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 762 · 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 notebooks cost ₹84, how much do 8 notebooks cost? (a) ₹126 (b) ₹86 (c) ₹672 (d) ₹112
2. 2.₹528 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹264 (b) ₹308 (c) ₹44 (d) ₹220
3. 3.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 9 days (d) 8 days
4. 4.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 13 days (d) 15 days
5. 5.If 2 kites cost ₹36, how much do 6 kites cost? (a) ₹108 (b) ₹40 (c) ₹126 (d) ₹216
6. 6.₹259 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹74 (b) ₹185 (c) ₹222 (d) ₹37
7. 7.If 2 notebooks cost ₹8, how much do 3 notebooks cost? (a) ₹16 (b) ₹9 (c) ₹24 (d) ₹12
8. 8.If 9 mangoes cost ₹135, how much do 4 mangoes cost? (a) ₹540 (b) ₹75 (c) ₹130 (d) ₹60
9. 9.If 4 notebooks cost ₹40, how much do 11 notebooks cost? (a) ₹440 (b) ₹120 (c) ₹47 (d) ₹110
10. 10.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 5 days (d) 6 days
11. 11.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 4 days (d) 12 days
12. 12.If 2 mangoes cost ₹44, how much do 11 mangoes cost? (a) ₹53 (b) ₹484 (c) ₹242 (d) ₹264
13. 13.₹480 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹40 (b) ₹200 (c) ₹240 (d) ₹280
14. 14.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 13 days (c) 29 days (d) 3 days
15. 15.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 4 days (d) 11 days
16. 16.If 8 kites cost ₹64, how much do 6 kites cost? (a) ₹62 (b) ₹56 (c) ₹384 (d) ₹48
17. 17.If 6 kites cost ₹78, how much do 2 kites cost? (a) ₹74 (b) ₹156 (c) ₹26 (d) ₹39
18. 18.₹180 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹40 (b) ₹90 (c) ₹140 (d) ₹20
19. 19.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 7 days (d) 9 days
20. 20.If 8 mangoes cost ₹144, how much do 6 mangoes cost? (a) ₹108 (b) ₹142 (c) ₹864 (d) ₹126
21. 21.If 7 mangoes cost ₹161, how much do 12 mangoes cost? (a) ₹166 (b) ₹299 (c) ₹1932 (d) ₹276
22. 22.If 7 notebooks cost ₹63, how much do 4 notebooks cost? (a) ₹60 (b) ₹252 (c) ₹45 (d) ₹36
23. 23.If 6 kites cost ₹24, how much do 3 kites cost? (a) ₹21 (b) ₹12 (c) ₹16 (d) ₹72
24. 24.If 3 kites cost ₹45, how much do 4 kites cost? (a) ₹180 (b) ₹60 (c) ₹46 (d) ₹75
25. 25.If 2 mangoes cost ₹16, how much do 11 mangoes cost? (a) ₹96 (b) ₹176 (c) ₹88 (d) ₹25
26. 26.If 6 mangoes cost ₹42, how much do 10 mangoes cost? (a) ₹46 (b) ₹420 (c) ₹77 (d) ₹70
27. 27.₹258 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹215 (b) ₹129 (c) ₹43 (d) ₹258
28. 28.If 3 kites cost ₹69, how much do 9 kites cost? (a) ₹230 (b) ₹621 (c) ₹75 (d) ₹207
29. 29.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 6 days (d) 10 days
30. 30.If 3 kites cost ₹33, how much do 12 kites cost? (a) ₹132 (b) ₹42 (c) ₹396 (d) ₹143
31. 31.₹440 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹44 (b) ₹132 (c) ₹220 (d) ₹308
32. 32.If 3 notebooks cost ₹12, how much do 6 notebooks cost? (a) ₹24 (b) ₹72 (c) ₹15 (d) ₹28
33. 33.If 5 pens cost ₹20, how much do 2 pens cost? (a) ₹8 (b) ₹12 (c) ₹40 (d) ₹17
34. 34.If 8 mangoes cost ₹144, how much do 2 mangoes cost? (a) ₹54 (b) ₹138 (c) ₹36 (d) ₹288
35. 35.₹110 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹90 (b) ₹10 (c) ₹20 (d) ₹55
36. 36.If 4 kites cost ₹20, how much do 10 kites cost? (a) ₹200 (b) ₹50 (c) ₹55 (d) ₹26
37. 37.₹442 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹306 (b) ₹136 (c) ₹221 (d) ₹34
38. 38.₹153 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹17 (b) ₹102 (c) ₹85 (d) ₹68
39. 39.If 7 notebooks cost ₹119, how much do 6 notebooks cost? (a) ₹118 (b) ₹119 (c) ₹102 (d) ₹714
40. 40.₹88 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹44 (b) ₹77 (c) ₹88 (d) ₹11

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