Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 50 · 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 7 pens cost ₹63, how much do 11 pens cost? (a) ₹108 (b) ₹99 (c) ₹67 (d) ₹693
2. 2.₹25 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹5 (b) ₹20 (c) ₹25 (d) ₹21
3. 3.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 7 days (d) 10 days
4. 4.₹572 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹352 (b) ₹220 (c) ₹286 (d) ₹44
5. 5.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 18 days (b) 3 days (c) 4 days (d) 5 days
6. 6.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 11 days (d) 1 day
7. 7.If 7 notebooks cost ₹91, how much do 8 notebooks cost? (a) ₹117 (b) ₹104 (c) ₹728 (d) ₹92
8. 8.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 14 days (c) 4 days (d) 15 days
9. 9.₹21 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹15 (b) ₹14 (c) ₹7 (d) ₹21
10. 10.₹242 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹121 (b) ₹22 (c) ₹44 (d) ₹198
11. 11.₹429 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹156 (b) ₹273 (c) ₹312 (d) ₹39
12. 12.₹216 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹36 (b) ₹216 (c) ₹180 (d) ₹108
13. 13.₹343 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹49 (b) ₹294 (c) ₹343 (d) ₹295
14. 14.If 6 mangoes cost ₹102, how much do 9 mangoes cost? (a) ₹170 (b) ₹918 (c) ₹105 (d) ₹153
15. 15.If 8 notebooks cost ₹120, how much do 5 notebooks cost? (a) ₹117 (b) ₹600 (c) ₹75 (d) ₹90
16. 16.₹242 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹154 (b) ₹121 (c) ₹22 (d) ₹88
17. 17.₹370 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹333 (b) ₹37 (c) ₹185 (d) ₹370
18. 18.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 48 days (c) 3 days (d) 6 days
19. 19.If 7 pens cost ₹98, how much do 2 pens cost? (a) ₹28 (b) ₹93 (c) ₹196 (d) ₹42
20. 20.If 7 pens cost ₹133, how much do 8 pens cost? (a) ₹1064 (b) ₹171 (c) ₹152 (d) ₹134
21. 21.₹132 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹12 (b) ₹36 (c) ₹96 (d) ₹66
22. 22.If 2 pens cost ₹6, how much do 7 pens cost? (a) ₹11 (b) ₹42 (c) ₹24 (d) ₹21
23. 23.If 4 kites cost ₹92, how much do 11 kites cost? (a) ₹99 (b) ₹1012 (c) ₹253 (d) ₹276
24. 24.₹442 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹306 (b) ₹136 (c) ₹221 (d) ₹34
25. 25.If 2 mangoes cost ₹38, how much do 10 mangoes cost? (a) ₹46 (b) ₹209 (c) ₹190 (d) ₹380
26. 26.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 1 day (c) 13 days (d) 21 days
27. 27.If 7 notebooks cost ₹154, how much do 4 notebooks cost? (a) ₹151 (b) ₹88 (c) ₹110 (d) ₹616
28. 28.If 7 mangoes cost ₹70, how much do 9 mangoes cost? (a) ₹72 (b) ₹630 (c) ₹100 (d) ₹90
29. 29.If 2 mangoes cost ₹20, how much do 8 mangoes cost? (a) ₹26 (b) ₹90 (c) ₹160 (d) ₹80
30. 30.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 11 days (c) 16 days (d) 4 days
31. 31.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 2 days (d) 3 days
32. 32.If 7 notebooks cost ₹175, how much do 5 notebooks cost? (a) ₹875 (b) ₹150 (c) ₹125 (d) ₹173
33. 33.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 11 days (d) 7 days
34. 34.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 9 days (d) 8 days
35. 35.₹297 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹81 (b) ₹27 (c) ₹216 (d) ₹243
36. 36.₹189 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹81 (b) ₹27 (c) ₹135 (d) ₹108
37. 37.4 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) 15 days (d) 26 days
38. 38.₹369 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹328 (b) ₹41 (c) ₹82 (d) ₹287
39. 39.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 3 days
40. 40.If 8 mangoes cost ₹152, how much do 11 mangoes cost? (a) ₹1672 (b) ₹155 (c) ₹209 (d) ₹228

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