Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 898 · 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. 1.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 18 days (d) 6 days
2. 2.If 9 kites cost ₹81, how much do 10 kites cost? (a) ₹99 (b) ₹82 (c) ₹810 (d) ₹90
3. 3.If 9 kites cost ₹153, how much do 12 kites cost? (a) ₹221 (b) ₹204 (c) ₹156 (d) ₹1836
4. 4.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 9 days (c) 15 days (d) 5 days
5. 5.₹288 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹288 (b) ₹144 (c) ₹48 (d) ₹240
6. 6.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 15 days (d) 16 days
7. 7.If 7 notebooks cost ₹21, how much do 8 notebooks cost? (a) ₹22 (b) ₹168 (c) ₹24 (d) ₹27
8. 8.5 workers can build a wall in 12 days. How many days will 10 workers take, working at the same speed? (a) 24 days (b) 7 days (c) 17 days (d) 6 days
9. 9.If 3 mangoes cost ₹39, how much do 4 mangoes cost? (a) ₹40 (b) ₹156 (c) ₹52 (d) ₹65
10. 10.If 2 pens cost ₹20, how much do 3 pens cost? (a) ₹40 (b) ₹60 (c) ₹21 (d) ₹30
11. 11.₹104 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹8 (b) ₹40 (c) ₹52 (d) ₹64
12. 12.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 10 days (d) 3 days
13. 13.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 17 days (c) 4 days (d) 6 days
14. 14.If 8 pens cost ₹32, how much do 3 pens cost? (a) ₹27 (b) ₹96 (c) ₹16 (d) ₹12
15. 15.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 16 days (d) 12 days
16. 16.If 5 kites cost ₹45, how much do 8 kites cost? (a) ₹360 (b) ₹72 (c) ₹48 (d) ₹81
17. 17.₹700 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹50 (b) ₹350 (c) ₹250 (d) ₹450
18. 18.If 2 mangoes cost ₹34, how much do 3 mangoes cost? (a) ₹35 (b) ₹102 (c) ₹68 (d) ₹51
19. 19.If 8 pens cost ₹152, how much do 12 pens cost? (a) ₹1824 (b) ₹156 (c) ₹228 (d) ₹247
20. 20.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 45 days (d) 5 days
21. 21.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 26 days (c) 27 days (d) 15 days
22. 22.If 5 kites cost ₹45, how much do 9 kites cost? (a) ₹405 (b) ₹81 (c) ₹49 (d) ₹90
23. 23.If 6 mangoes cost ₹138, how much do 4 mangoes cost? (a) ₹136 (b) ₹92 (c) ₹115 (d) ₹552
24. 24.If 9 notebooks cost ₹54, how much do 8 notebooks cost? (a) ₹432 (b) ₹53 (c) ₹54 (d) ₹48
25. 25.₹532 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹38 (b) ₹266 (c) ₹342 (d) ₹190
26. 26.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 40 days (c) 39 days (d) 17 days
27. 27.If 6 mangoes cost ₹144, how much do 4 mangoes cost? (a) ₹142 (b) ₹120 (c) ₹576 (d) ₹96
28. 28.₹280 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹120 (b) ₹140 (c) ₹160 (d) ₹40
29. 29.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 35 days (b) 19 days (c) 11 days (d) 36 days
30. 30.₹288 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹144 (b) ₹32 (c) ₹64 (d) ₹224
31. 31.₹176 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹22 (b) ₹88 (c) ₹176 (d) ₹154
32. 32.₹84 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹54 (b) ₹30 (c) ₹6 (d) ₹42
33. 33.₹140 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹70 (b) ₹140 (c) ₹20 (d) ₹120
34. 34.₹130 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹50 (b) ₹10 (c) ₹80 (d) ₹65
35. 35.If 5 kites cost ₹35, how much do 2 kites cost? (a) ₹70 (b) ₹14 (c) ₹32 (d) ₹21
36. 36.₹221 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹68 (b) ₹153 (c) ₹17 (d) ₹170
37. 37.₹195 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹75 (b) ₹15 (c) ₹120 (d) ₹135
38. 38.₹315 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹280 (b) ₹70 (c) ₹35 (d) ₹245
39. 39.If 4 notebooks cost ₹44, how much do 9 notebooks cost? (a) ₹99 (b) ₹49 (c) ₹110 (d) ₹396
40. 40.₹230 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹161 (b) ₹23 (c) ₹69 (d) ₹115

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