Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 777 · 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.₹168 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹105 (b) ₹84 (c) ₹63 (d) ₹21
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) 5 days (d) 21 days
3. 3.₹370 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹185 (b) ₹259 (c) ₹37 (d) ₹111
4. 4.₹294 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹42 (b) ₹147 (c) ₹210 (d) ₹84
5. 5.If 6 notebooks cost ₹60, how much do 2 notebooks cost? (a) ₹20 (b) ₹56 (c) ₹120 (d) ₹30
6. 6.₹231 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹33 (b) ₹165 (c) ₹66 (d) ₹198
7. 7.If 7 pens cost ₹49, how much do 6 pens cost? (a) ₹294 (b) ₹42 (c) ₹48 (d) ₹49
8. 8.₹490 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹245 (b) ₹315 (c) ₹35 (d) ₹175
9. 9.₹91 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹79 (b) ₹91 (c) ₹13 (d) ₹78
10. 10.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 9 days
11. 11.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 3 days (c) 2 days (d) 4 days
12. 12.₹75 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹75 (b) ₹61 (c) ₹60 (d) ₹15
13. 13.If 2 kites cost ₹16, how much do 5 kites cost? (a) ₹40 (b) ₹19 (c) ₹80 (d) ₹48
14. 14.If 6 kites cost ₹78, how much do 3 kites cost? (a) ₹75 (b) ₹234 (c) ₹39 (d) ₹52
15. 15.₹112 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹56 (b) ₹98 (c) ₹112 (d) ₹14
16. 16.₹315 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹35 (b) ₹70 (c) ₹245 (d) ₹280
17. 17.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 11 days (d) 7 days
18. 18.If 2 pens cost ₹32, how much do 11 pens cost? (a) ₹192 (b) ₹41 (c) ₹352 (d) ₹176
19. 19.₹266 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹95 (b) ₹133 (c) ₹19 (d) ₹171
20. 20.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 40 days (c) 7 days (d) 39 days
21. 21.₹585 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹225 (b) ₹45 (c) ₹405 (d) ₹360
22. 22.₹90 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹10 (b) ₹90 (c) ₹80 (d) ₹45
23. 23.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 3 days (d) 10 days
24. 24.If 2 pens cost ₹26, how much do 3 pens cost? (a) ₹78 (b) ₹52 (c) ₹27 (d) ₹39
25. 25.If 6 notebooks cost ₹138, how much do 4 notebooks cost? (a) ₹552 (b) ₹136 (c) ₹115 (d) ₹92
26. 26.₹414 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹184 (b) ₹46 (c) ₹230 (d) ₹207
27. 27.If 9 mangoes cost ₹99, how much do 6 mangoes cost? (a) ₹77 (b) ₹594 (c) ₹96 (d) ₹66
28. 28.6 workers can build a wall in 14 days. How many days will 12 workers take, working at the same speed? (a) 8 days (b) 20 days (c) 28 days (d) 7 days
29. 29.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 7 days
30. 30.₹320 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹280 (b) ₹320 (c) ₹160 (d) ₹40
31. 31.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 1 day (d) 13 days
32. 32.₹66 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹44 (b) ₹22 (c) ₹66 (d) ₹33
33. 33.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 16 days (c) 15 days (d) 9 days
34. 34.₹390 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹39 (b) ₹273 (c) ₹195 (d) ₹117
35. 35.If 5 pens cost ₹60, how much do 8 pens cost? (a) ₹63 (b) ₹108 (c) ₹480 (d) ₹96
36. 36.₹112 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹56 (b) ₹8 (c) ₹40 (d) ₹72
37. 37.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 21 days (d) 22 days
38. 38.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 52 days (b) 19 days (c) 7 days (d) 53 days
39. 39.If 7 pens cost ₹91, how much do 12 pens cost? (a) ₹96 (b) ₹169 (c) ₹156 (d) ₹1092
40. 40.If 4 pens cost ₹12, how much do 5 pens cost? (a) ₹60 (b) ₹18 (c) ₹13 (d) ₹15

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