Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 883 · 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 3 pens cost ₹15, how much do 2 pens cost? (a) ₹14 (b) ₹15 (c) ₹10 (d) ₹30
2. 2.If 3 notebooks cost ₹69, how much do 11 notebooks cost? (a) ₹276 (b) ₹77 (c) ₹759 (d) ₹253
3. 3.If 9 pens cost ₹225, how much do 7 pens cost? (a) ₹175 (b) ₹1575 (c) ₹200 (d) ₹223
4. 4.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 3 days (d) 6 days
5. 5.₹135 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹135 (b) ₹109 (c) ₹108 (d) ₹27
6. 6.₹360 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹180 (b) ₹108 (c) ₹36 (d) ₹252
7. 7.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 2 days (d) 1 day
8. 8.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 4 days (d) 2 days
9. 9.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 9 days (d) 25 days
10. 10.If 3 kites cost ₹33, how much do 6 kites cost? (a) ₹77 (b) ₹36 (c) ₹198 (d) ₹66
11. 11.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 7 days (c) 40 days (d) 39 days
12. 12.If 4 pens cost ₹40, how much do 5 pens cost? (a) ₹200 (b) ₹50 (c) ₹41 (d) ₹60
13. 13.If 4 kites cost ₹80, how much do 12 kites cost? (a) ₹260 (b) ₹960 (c) ₹240 (d) ₹88
14. 14.₹217 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹93 (b) ₹155 (c) ₹31 (d) ₹124
15. 15.If 3 kites cost ₹27, how much do 4 kites cost? (a) ₹108 (b) ₹45 (c) ₹36 (d) ₹28
16. 16.If 4 pens cost ₹40, how much do 3 pens cost? (a) ₹39 (b) ₹30 (c) ₹40 (d) ₹120
17. 17.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 64 days (b) 7 days (c) 63 days (d) 21 days
18. 18.If 2 mangoes cost ₹20, how much do 3 mangoes cost? (a) ₹40 (b) ₹30 (c) ₹21 (d) ₹60
19. 19.6 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 2 days (c) 14 days (d) 4 days
20. 20.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 17 days (d) 1 day
21. 21.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 8 days (d) 2 days
22. 22.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 13 days (c) 22 days (d) 9 days
23. 23.If 3 pens cost ₹42, how much do 6 pens cost? (a) ₹84 (b) ₹252 (c) ₹98 (d) ₹45
24. 24.₹168 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹84 (b) ₹24 (c) ₹120 (d) ₹48
25. 25.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 15 days (d) 14 days
26. 26.₹200 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹100 (b) ₹125 (c) ₹25 (d) ₹75
27. 27.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 17 days (c) 3 days (d) 27 days
28. 28.If 3 kites cost ₹9, how much do 8 kites cost? (a) ₹72 (b) ₹14 (c) ₹27 (d) ₹24
29. 29.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 11 days (d) 4 days
30. 30.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 11 days (c) 20 days (d) 19 days
31. 31.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 11 days (d) 2 days
32. 32.₹546 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹351 (b) ₹39 (c) ₹273 (d) ₹195
33. 33.If 9 mangoes cost ₹144, how much do 12 mangoes cost? (a) ₹208 (b) ₹192 (c) ₹147 (d) ₹1728
34. 34.If 3 notebooks cost ₹21, how much do 5 notebooks cost? (a) ₹105 (b) ₹23 (c) ₹35 (d) ₹42
35. 35.3 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 5 days (d) 11 days
36. 36.If 8 pens cost ₹200, how much do 2 pens cost? (a) ₹194 (b) ₹50 (c) ₹400 (d) ₹75
37. 37.₹360 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹180 (b) ₹36 (c) ₹360 (d) ₹324
38. 38.If 9 notebooks cost ₹162, how much do 6 notebooks cost? (a) ₹108 (b) ₹972 (c) ₹126 (d) ₹159
39. 39.₹115 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹46 (b) ₹23 (c) ₹92 (d) ₹69
40. 40.If 5 notebooks cost ₹35, how much do 7 notebooks cost? (a) ₹37 (b) ₹245 (c) ₹56 (d) ₹49

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