Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 96 · 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 kites cost ₹102, how much do 9 kites cost? (a) ₹105 (b) ₹918 (c) ₹170 (d) ₹153
2. 2.If 2 mangoes cost ₹38, how much do 4 mangoes cost? (a) ₹152 (b) ₹95 (c) ₹76 (d) ₹40
3. 3.If 3 pens cost ₹60, how much do 12 pens cost? (a) ₹240 (b) ₹260 (c) ₹720 (d) ₹69
4. 4.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 10 days (c) 3 days (d) 4 days
5. 5.₹42 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹21 (b) ₹36 (c) ₹6 (d) ₹42
6. 6.₹150 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹75 (b) ₹30 (c) ₹90 (d) ₹60
7. 7.If 3 notebooks cost ₹48, how much do 6 notebooks cost? (a) ₹51 (b) ₹96 (c) ₹112 (d) ₹288
8. 8.If 5 kites cost ₹30, how much do 9 kites cost? (a) ₹54 (b) ₹270 (c) ₹60 (d) ₹34
9. 9.If 5 kites cost ₹40, how much do 11 kites cost? (a) ₹440 (b) ₹46 (c) ₹96 (d) ₹88
10. 10.If 9 mangoes cost ₹99, how much do 3 mangoes cost? (a) ₹33 (b) ₹93 (c) ₹44 (d) ₹297
11. 11.If 2 pens cost ₹18, how much do 6 pens cost? (a) ₹63 (b) ₹22 (c) ₹54 (d) ₹108
12. 12.If 7 pens cost ₹112, how much do 5 pens cost? (a) ₹110 (b) ₹560 (c) ₹80 (d) ₹96
13. 13.₹235 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹188 (b) ₹47 (c) ₹235 (d) ₹189
14. 14.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 42 days (b) 43 days (c) 10 days (d) 18 days
15. 15.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 7 days (d) 6 days
16. 16.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 11 days (c) 5 days (d) 20 days
17. 17.6 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) 9 days (d) 16 days
18. 18.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 7 days (d) 6 days
19. 19.₹240 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹120 (b) ₹240 (c) ₹24 (d) ₹216
20. 20.If 5 notebooks cost ₹35, how much do 12 notebooks cost? (a) ₹91 (b) ₹84 (c) ₹420 (d) ₹42
21. 21.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 24 days (c) 15 days (d) 9 days
22. 22.₹600 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹350 (b) ₹300 (c) ₹250 (d) ₹50
23. 23.₹539 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹147 (b) ₹49 (c) ₹392 (d) ₹441
24. 24.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 11 days (d) 1 day
25. 25.If 8 pens cost ₹48, how much do 2 pens cost? (a) ₹96 (b) ₹18 (c) ₹42 (d) ₹12
26. 26.If 2 pens cost ₹48, how much do 3 pens cost? (a) ₹144 (b) ₹72 (c) ₹49 (d) ₹96
27. 27.₹112 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹28 (b) ₹84 (c) ₹56 (d) ₹112
28. 28.₹60 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹20 (b) ₹30 (c) ₹60 (d) ₹40
29. 29.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 35 days (b) 11 days (c) 36 days (d) 19 days
30. 30.If 3 pens cost ₹39, how much do 4 pens cost? (a) ₹65 (b) ₹156 (c) ₹52 (d) ₹40
31. 31.₹55 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹5 (b) ₹20 (c) ₹35 (d) ₹40
32. 32.₹390 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹195 (b) ₹270 (c) ₹120 (d) ₹30
33. 33.If 6 pens cost ₹18, how much do 12 pens cost? (a) ₹24 (b) ₹216 (c) ₹39 (d) ₹36
34. 34.₹315 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹245 (b) ₹280 (c) ₹70 (d) ₹35
35. 35.₹141 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹141 (b) ₹95 (c) ₹47 (d) ₹94
36. 36.₹264 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹72 (b) ₹192 (c) ₹132 (d) ₹24
37. 37.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 17 days (d) 5 days
38. 38.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 24 days (c) 14 days (d) 25 days
39. 39.₹650 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹400 (b) ₹325 (c) ₹50 (d) ₹250
40. 40.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 28 days (c) 7 days (d) 16 days

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