Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 277 · 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.₹180 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹15 (b) ₹90 (c) ₹75 (d) ₹105
2. 2.₹480 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹280 (b) ₹40 (c) ₹200 (d) ₹240
3. 3.₹150 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹150 (b) ₹75 (c) ₹30 (d) ₹120
4. 4.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 13 days (c) 4 days (d) 25 days
5. 5.₹287 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹246 (b) ₹41 (c) ₹82 (d) ₹205
6. 6.If 9 mangoes cost ₹189, how much do 10 mangoes cost? (a) ₹1890 (b) ₹231 (c) ₹210 (d) ₹190
7. 7.₹368 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹368 (b) ₹46 (c) ₹322 (d) ₹184
8. 8.9 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 11 days
9. 9.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 15 days (d) 28 days
10. 10.₹225 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹45 (b) ₹90 (c) ₹180 (d) ₹135
11. 11.6 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 31 days (b) 30 days (c) 6 days (d) 14 days
12. 12.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 11 days (d) 15 days
13. 13.If 6 mangoes cost ₹90, how much do 12 mangoes cost? (a) ₹96 (b) ₹195 (c) ₹1080 (d) ₹180
14. 14.If 4 kites cost ₹84, how much do 8 kites cost? (a) ₹88 (b) ₹189 (c) ₹168 (d) ₹672
15. 15.₹132 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹132 (b) ₹99 (c) ₹66 (d) ₹33
16. 16.If 9 kites cost ₹72, how much do 4 kites cost? (a) ₹67 (b) ₹288 (c) ₹40 (d) ₹32
17. 17.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 12 days (c) 13 days (d) 11 days
18. 18.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 4 days (d) 9 days
19. 19.₹154 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹28 (b) ₹77 (c) ₹126 (d) ₹14
20. 20.₹242 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹22 (b) ₹121 (c) ₹132 (d) ₹110
21. 21.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 13 days (b) 1 day (c) 16 days (d) 2 days
22. 22.₹451 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹82 (b) ₹41 (c) ₹410 (d) ₹369
23. 23.₹102 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹68 (b) ₹102 (c) ₹34 (d) ₹51
24. 24.If 4 notebooks cost ₹32, how much do 3 notebooks cost? (a) ₹32 (b) ₹96 (c) ₹24 (d) ₹31
25. 25.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 5 days (c) 44 days (d) 17 days
26. 26.₹174 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹29 (b) ₹174 (c) ₹145 (d) ₹87
27. 27.₹175 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹25 (b) ₹50 (c) ₹150 (d) ₹125
28. 28.₹294 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹147 (b) ₹252 (c) ₹42 (d) ₹294
29. 29.₹50 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹10 (c) ₹25 (d) ₹30
30. 30.If 8 notebooks cost ₹128, how much do 10 notebooks cost? (a) ₹1280 (b) ₹160 (c) ₹130 (d) ₹176
31. 31.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 8 days (c) 13 days (d) 11 days
32. 32.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 28 days (b) 11 days (c) 17 days (d) 7 days
33. 33.If 6 notebooks cost ₹42, how much do 4 notebooks cost? (a) ₹168 (b) ₹28 (c) ₹40 (d) ₹35
34. 34.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 19 days (c) 3 days (d) 4 days
35. 35.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 11 days (c) 26 days (d) 15 days
36. 36.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 12 days (d) 11 days
37. 37.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 43 days (b) 17 days (c) 7 days (d) 42 days
38. 38.₹322 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹161 (b) ₹230 (c) ₹92 (d) ₹46
39. 39.If 4 mangoes cost ₹16, how much do 11 mangoes cost? (a) ₹176 (b) ₹23 (c) ₹48 (d) ₹44
40. 40.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 4 days (c) 15 days (d) 3 days

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