Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 495 · 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. 1.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 4 days (d) 5 days
2. 2.₹72 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹36 (b) ₹40 (c) ₹32 (d) ₹8
3. 3.₹559 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹43 (b) ₹387 (c) ₹172 (d) ₹430
4. 4.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 5 days (d) 20 days
5. 5.If 9 kites cost ₹45, how much do 3 kites cost? (a) ₹135 (b) ₹39 (c) ₹20 (d) ₹15
6. 6.If 3 kites cost ₹27, how much do 9 kites cost? (a) ₹90 (b) ₹33 (c) ₹243 (d) ₹81
7. 7.If 4 notebooks cost ₹40, how much do 11 notebooks cost? (a) ₹110 (b) ₹120 (c) ₹440 (d) ₹47
8. 8.If 2 kites cost ₹6, how much do 6 kites cost? (a) ₹18 (b) ₹36 (c) ₹10 (d) ₹21
9. 9.If 3 pens cost ₹30, how much do 5 pens cost? (a) ₹150 (b) ₹50 (c) ₹60 (d) ₹32
10. 10.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 27 days (c) 26 days (d) 15 days
11. 11.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 10 days (d) 5 days
12. 12.₹78 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹48 (b) ₹6 (c) ₹30 (d) ₹39
13. 13.If 6 kites cost ₹90, how much do 3 kites cost? (a) ₹60 (b) ₹45 (c) ₹87 (d) ₹270
14. 14.₹637 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹441 (b) ₹245 (c) ₹392 (d) ₹49
15. 15.₹312 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹26 (b) ₹156 (c) ₹182 (d) ₹130
16. 16.₹506 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹414 (b) ₹92 (c) ₹46 (d) ₹253
17. 17.₹400 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹150 (b) ₹50 (c) ₹250 (d) ₹200
18. 18.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 3 days (d) 2 days
19. 19.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 6 days (d) 24 days
20. 20.₹658 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹235 (b) ₹47 (c) ₹329 (d) ₹423
21. 21.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 5 days (d) 4 days
22. 22.If 5 mangoes cost ₹40, how much do 12 mangoes cost? (a) ₹96 (b) ₹480 (c) ₹47 (d) ₹104
23. 23.₹378 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹243 (b) ₹135 (c) ₹189 (d) ₹27
24. 24.If 5 notebooks cost ₹100, how much do 3 notebooks cost? (a) ₹80 (b) ₹98 (c) ₹300 (d) ₹60
25. 25.₹129 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹129 (b) ₹87 (c) ₹86 (d) ₹43
26. 26.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹40 (b) ₹48 (c) ₹8 (d) ₹44
27. 27.₹546 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹351 (b) ₹39 (c) ₹195 (d) ₹273
28. 28.If 9 notebooks cost ₹27, how much do 12 notebooks cost? (a) ₹39 (b) ₹36 (c) ₹324 (d) ₹30
29. 29.4 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
30. 30.₹24 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹24 (b) ₹12 (c) ₹18 (d) ₹6
31. 31.If 8 kites cost ₹144, how much do 12 kites cost? (a) ₹216 (b) ₹148 (c) ₹234 (d) ₹1728
32. 32.If 6 notebooks cost ₹120, how much do 4 notebooks cost? (a) ₹480 (b) ₹118 (c) ₹80 (d) ₹100
33. 33.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 28 days (c) 19 days (d) 9 days
34. 34.If 5 mangoes cost ₹20, how much do 4 mangoes cost? (a) ₹19 (b) ₹20 (c) ₹80 (d) ₹16
35. 35.₹175 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹75 (b) ₹25 (c) ₹100 (d) ₹125
36. 36.If 8 notebooks cost ₹40, how much do 2 notebooks cost? (a) ₹15 (b) ₹34 (c) ₹80 (d) ₹10
37. 37.If 5 pens cost ₹120, how much do 12 pens cost? (a) ₹288 (b) ₹127 (c) ₹312 (d) ₹1440
38. 38.₹552 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹230 (b) ₹46 (c) ₹276 (d) ₹322
39. 39.If 7 kites cost ₹42, how much do 10 kites cost? (a) ₹60 (b) ₹420 (c) ₹45 (d) ₹66
40. 40.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 9 days (d) 4 days

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