Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 870 · 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 2 mangoes cost ₹24, how much do 4 mangoes cost? (a) ₹48 (b) ₹96 (c) ₹60 (d) ₹26
2. 2.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 3 days (d) 10 days
3. 3.If 3 mangoes cost ₹60, how much do 7 mangoes cost? (a) ₹420 (b) ₹160 (c) ₹140 (d) ₹64
4. 4.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 21 days (c) 5 days (d) 22 days
5. 5.If 9 kites cost ₹225, how much do 11 kites cost? (a) ₹227 (b) ₹275 (c) ₹300 (d) ₹2475
6. 6.If 7 pens cost ₹175, how much do 5 pens cost? (a) ₹150 (b) ₹875 (c) ₹125 (d) ₹173
7. 7.₹187 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹136 (b) ₹17 (c) ₹153 (d) ₹51
8. 8.If 2 notebooks cost ₹44, how much do 3 notebooks cost? (a) ₹45 (b) ₹132 (c) ₹66 (d) ₹88
9. 9.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 14 days (b) 16 days (c) 13 days (d) 12 days
10. 10.If 7 pens cost ₹49, how much do 10 pens cost? (a) ₹70 (b) ₹490 (c) ₹77 (d) ₹52
11. 11.If 8 pens cost ₹80, how much do 10 pens cost? (a) ₹800 (b) ₹82 (c) ₹100 (d) ₹110
12. 12.₹110 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹30 (b) ₹55 (c) ₹10 (d) ₹80
13. 13.₹460 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹46 (b) ₹230 (c) ₹138 (d) ₹322
14. 14.₹99 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹66 (b) ₹33 (c) ₹67 (d) ₹99
15. 15.₹102 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹51 (b) ₹102 (c) ₹68 (d) ₹34
16. 16.₹637 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹490 (b) ₹441 (c) ₹49 (d) ₹196
17. 17.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 2 days (d) 3 days
18. 18.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 4 days (d) 5 days
19. 19.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 10 days (c) 3 days (d) 9 days
20. 20.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 7 days (d) 6 days
21. 21.If 7 pens cost ₹70, how much do 3 pens cost? (a) ₹30 (b) ₹66 (c) ₹210 (d) ₹40
22. 22.₹266 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹133 (b) ₹171 (c) ₹95 (d) ₹19
23. 23.If 6 mangoes cost ₹114, how much do 4 mangoes cost? (a) ₹76 (b) ₹112 (c) ₹95 (d) ₹456
24. 24.If 2 kites cost ₹10, how much do 6 kites cost? (a) ₹35 (b) ₹14 (c) ₹30 (d) ₹60
25. 25.If 4 notebooks cost ₹80, how much do 3 notebooks cost? (a) ₹79 (b) ₹240 (c) ₹60 (d) ₹80
26. 26.6 workers can build a wall in 14 days. How many days will 12 workers take, working at the same speed? (a) 20 days (b) 28 days (c) 8 days (d) 7 days
27. 27.₹414 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹46 (b) ₹230 (c) ₹207 (d) ₹184
28. 28.₹30 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹24 (b) ₹30 (c) ₹6 (d) ₹15
29. 29.If 4 kites cost ₹76, how much do 11 kites cost? (a) ₹83 (b) ₹836 (c) ₹228 (d) ₹209
30. 30.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 1 day (d) 7 days
31. 31.₹228 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹95 (b) ₹114 (c) ₹19 (d) ₹133
32. 32.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹12 (b) ₹60 (c) ₹84 (d) ₹108
33. 33.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 10 days (d) 11 days
34. 34.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 3 days (d) 7 days
35. 35.₹56 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹16 (b) ₹8 (c) ₹28 (d) ₹40
36. 36.If 5 notebooks cost ₹25, how much do 10 notebooks cost? (a) ₹55 (b) ₹50 (c) ₹250 (d) ₹30
37. 37.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 16 days (d) 20 days
38. 38.5 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 31 days (d) 30 days
39. 39.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 4 days (c) 16 days (d) 41 days
40. 40.₹611 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹423 (b) ₹47 (c) ₹235 (d) ₹376

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