Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 770 · 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.₹93 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹93 (b) ₹63 (c) ₹31 (d) ₹62
2. 2.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 45 days (c) 21 days (d) 5 days
3. 3.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 4 days (c) 3 days (d) 12 days
4. 4.₹392 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹28 (b) ₹196 (c) ₹252 (d) ₹140
5. 5.If 3 mangoes cost ₹54, how much do 4 mangoes cost? (a) ₹55 (b) ₹90 (c) ₹72 (d) ₹216
6. 6.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 25 days (c) 23 days (d) 24 days
7. 7.₹117 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹104 (b) ₹13 (c) ₹26 (d) ₹91
8. 8.If 3 notebooks cost ₹57, how much do 4 notebooks cost? (a) ₹95 (b) ₹228 (c) ₹76 (d) ₹58
9. 9.8 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 2 days (c) 8 days (d) 7 days
10. 10.If 2 kites cost ₹20, how much do 12 kites cost? (a) ₹130 (b) ₹120 (c) ₹240 (d) ₹30
11. 11.₹450 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹225 (b) ₹350 (c) ₹100 (d) ₹50
12. 12.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 14 days (d) 9 days
13. 13.₹78 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹78 (b) ₹26 (c) ₹52 (d) ₹39
14. 14.₹40 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹8 (c) ₹16 (d) ₹24
15. 15.If 5 notebooks cost ₹80, how much do 6 notebooks cost? (a) ₹81 (b) ₹96 (c) ₹480 (d) ₹112
16. 16.If 5 notebooks cost ₹15, how much do 4 notebooks cost? (a) ₹14 (b) ₹60 (c) ₹15 (d) ₹12
17. 17.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 8 days (c) 12 days (d) 20 days
18. 18.If 9 notebooks cost ₹180, how much do 6 notebooks cost? (a) ₹177 (b) ₹140 (c) ₹1080 (d) ₹120
19. 19.If 4 mangoes cost ₹36, how much do 2 mangoes cost? (a) ₹34 (b) ₹18 (c) ₹72 (d) ₹27
20. 20.If 6 kites cost ₹102, how much do 8 kites cost? (a) ₹104 (b) ₹816 (c) ₹153 (d) ₹136
21. 21.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 16 days (d) 17 days
22. 22.4 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
23. 23.₹185 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹74 (b) ₹111 (c) ₹37 (d) ₹148
24. 24.If 2 notebooks cost ₹46, how much do 3 notebooks cost? (a) ₹92 (b) ₹69 (c) ₹47 (d) ₹138
25. 25.₹190 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹95 (b) ₹152 (c) ₹38 (d) ₹190
26. 26.₹637 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹196 (b) ₹490 (c) ₹49 (d) ₹441
27. 27.If 4 kites cost ₹84, how much do 5 kites cost? (a) ₹105 (b) ₹126 (c) ₹85 (d) ₹420
28. 28.If 9 notebooks cost ₹108, how much do 4 notebooks cost? (a) ₹60 (b) ₹48 (c) ₹103 (d) ₹432
29. 29.If 3 kites cost ₹9, how much do 10 kites cost? (a) ₹16 (b) ₹33 (c) ₹30 (d) ₹90
30. 30.If 6 mangoes cost ₹78, how much do 2 mangoes cost? (a) ₹74 (b) ₹156 (c) ₹26 (d) ₹39
31. 31.If 2 pens cost ₹28, how much do 4 pens cost? (a) ₹30 (b) ₹56 (c) ₹70 (d) ₹112
32. 32.If 3 pens cost ₹15, how much do 5 pens cost? (a) ₹25 (b) ₹17 (c) ₹30 (d) ₹75
33. 33.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 18 days (d) 5 days
34. 34.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 22 days (b) 15 days (c) 7 days (d) 23 days
35. 35.If 4 mangoes cost ₹80, how much do 2 mangoes cost? (a) ₹160 (b) ₹78 (c) ₹60 (d) ₹40
36. 36.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 7 days (c) 13 days (d) 16 days
37. 37.₹70 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹20 (b) ₹10 (c) ₹35 (d) ₹50
38. 38.If 6 notebooks cost ₹150, how much do 12 notebooks cost? (a) ₹156 (b) ₹1800 (c) ₹325 (d) ₹300
39. 39.If 6 pens cost ₹132, how much do 3 pens cost? (a) ₹88 (b) ₹66 (c) ₹396 (d) ₹129
40. 40.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 33 days (c) 34 days (d) 17 days

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