Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 402 · 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 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 4 days (d) 5 days
2. 2.₹132 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹36 (b) ₹12 (c) ₹96 (d) ₹66
3. 3.If 3 pens cost ₹48, how much do 9 pens cost? (a) ₹144 (b) ₹432 (c) ₹160 (d) ₹54
4. 4.₹114 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹57 (b) ₹114 (c) ₹76 (d) ₹38
5. 5.If 3 notebooks cost ₹30, how much do 7 notebooks cost? (a) ₹70 (b) ₹210 (c) ₹34 (d) ₹80
6. 6.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 8 days (d) 7 days
7. 7.₹78 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹6 (b) ₹39 (c) ₹48 (d) ₹30
8. 8.₹450 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹225 (b) ₹450 (c) ₹50 (d) ₹400
9. 9.If 3 notebooks cost ₹63, how much do 5 notebooks cost? (a) ₹126 (b) ₹65 (c) ₹315 (d) ₹105
10. 10.If 8 notebooks cost ₹184, how much do 9 notebooks cost? (a) ₹207 (b) ₹230 (c) ₹185 (d) ₹1656
11. 11.₹672 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹240 (b) ₹432 (c) ₹48 (d) ₹336
12. 12.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 12 days (c) 7 days (d) 6 days
13. 13.If 9 kites cost ₹216, how much do 10 kites cost? (a) ₹2160 (b) ₹264 (c) ₹240 (d) ₹217
14. 14.8 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 7 days (d) 2 days
15. 15.If 6 mangoes cost ₹132, how much do 2 mangoes cost? (a) ₹264 (b) ₹44 (c) ₹128 (d) ₹66
16. 16.₹308 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹196 (b) ₹154 (c) ₹28 (d) ₹112
17. 17.If 9 mangoes cost ₹180, how much do 12 mangoes cost? (a) ₹183 (b) ₹260 (c) ₹240 (d) ₹2160
18. 18.₹442 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹34 (b) ₹272 (c) ₹170 (d) ₹221
19. 19.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 9 days
20. 20.If 7 mangoes cost ₹119, how much do 8 mangoes cost? (a) ₹120 (b) ₹952 (c) ₹153 (d) ₹136
21. 21.If 2 notebooks cost ₹36, how much do 4 notebooks cost? (a) ₹144 (b) ₹90 (c) ₹72 (d) ₹38
22. 22.6 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 6 days (c) 10 days (d) 13 days
23. 23.If 7 pens cost ₹175, how much do 8 pens cost? (a) ₹1400 (b) ₹176 (c) ₹200 (d) ₹225
24. 24.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 5 days (d) 9 days
25. 25.If 5 kites cost ₹70, how much do 12 kites cost? (a) ₹168 (b) ₹840 (c) ₹182 (d) ₹77
26. 26.₹572 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹286 (b) ₹396 (c) ₹44 (d) ₹176
27. 27.If 8 notebooks cost ₹88, how much do 11 notebooks cost? (a) ₹132 (b) ₹91 (c) ₹968 (d) ₹121
28. 28.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 9 days (d) 1 day
29. 29.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 22 days (d) 21 days
30. 30.₹220 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹220 (b) ₹110 (c) ₹44 (d) ₹176
31. 31.₹171 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹95 (b) ₹76 (c) ₹19 (d) ₹114
32. 32.If 2 kites cost ₹26, how much do 8 kites cost? (a) ₹32 (b) ₹104 (c) ₹117 (d) ₹208
33. 33.₹180 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹90 (b) ₹105 (c) ₹75 (d) ₹15
34. 34.₹343 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹49 (b) ₹343 (c) ₹295 (d) ₹294
35. 35.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 15 days (c) 9 days (d) 13 days
36. 36.If 3 pens cost ₹30, how much do 11 pens cost? (a) ₹120 (b) ₹110 (c) ₹330 (d) ₹38
37. 37.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 48 days (c) 3 days (d) 18 days
38. 38.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 22 days (b) 17 days (c) 21 days (d) 11 days
39. 39.₹352 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹176 (b) ₹128 (c) ₹224 (d) ₹32
40. 40.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 24 days (c) 25 days (d) 12 days

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