Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 865 · 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 12 days. How many days will 6 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 9 days (d) 24 days
2. 2.8 workers can build a wall in 9 days. How many days will 4 workers take, working at the same speed? (a) 19 days (b) 5 days (c) 18 days (d) 13 days
3. 3.If 7 pens cost ₹77, how much do 2 pens cost? (a) ₹33 (b) ₹72 (c) ₹154 (d) ₹22
4. 4.6 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 14 days (b) 7 days (c) 6 days (d) 5 days
5. 5.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 2 days (d) 4 days
6. 6.₹294 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹21 (b) ₹105 (c) ₹147 (d) ₹189
7. 7.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 28 days (d) 17 days
8. 8.₹108 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹12 (b) ₹84 (c) ₹54 (d) ₹24
9. 9.If 8 pens cost ₹88, how much do 3 pens cost? (a) ₹33 (b) ₹44 (c) ₹264 (d) ₹83
10. 10.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 6 days (c) 4 days (d) 10 days
11. 11.If 8 notebooks cost ₹48, how much do 12 notebooks cost? (a) ₹576 (b) ₹52 (c) ₹78 (d) ₹72
12. 12.₹90 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹45 (b) ₹36 (c) ₹18 (d) ₹54
13. 13.If 8 pens cost ₹112, how much do 9 pens cost? (a) ₹1008 (b) ₹113 (c) ₹126 (d) ₹140
14. 14.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 6 days (c) 19 days (d) 12 days
15. 15.If 6 mangoes cost ₹24, how much do 7 mangoes cost? (a) ₹32 (b) ₹25 (c) ₹168 (d) ₹28
16. 16.₹30 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹6 (b) ₹30 (c) ₹24 (d) ₹15
17. 17.If 4 mangoes cost ₹12, how much do 2 mangoes cost? (a) ₹6 (b) ₹24 (c) ₹9 (d) ₹10
18. 18.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 18 days (c) 10 days (d) 11 days
19. 19.If 2 notebooks cost ₹12, how much do 11 notebooks cost? (a) ₹21 (b) ₹132 (c) ₹72 (d) ₹66
20. 20.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 3 days (d) 6 days
21. 21.If 4 notebooks cost ₹72, how much do 7 notebooks cost? (a) ₹126 (b) ₹144 (c) ₹75 (d) ₹504
22. 22.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 22 days (c) 21 days (d) 1 day
23. 23.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 9 days (d) 23 days
24. 24.₹266 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹190 (b) ₹38 (c) ₹76 (d) ₹133
25. 25.₹221 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹153 (b) ₹68 (c) ₹17 (d) ₹170
26. 26.If 2 kites cost ₹12, how much do 3 kites cost? (a) ₹24 (b) ₹13 (c) ₹36 (d) ₹18
27. 27.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 9 days (c) 4 days (d) 49 days
28. 28.₹66 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹33 (b) ₹12 (c) ₹6 (d) ₹54
29. 29.If 2 kites cost ₹36, how much do 5 kites cost? (a) ₹90 (b) ₹180 (c) ₹39 (d) ₹108
30. 30.If 4 mangoes cost ₹44, how much do 9 mangoes cost? (a) ₹99 (b) ₹110 (c) ₹396 (d) ₹49
31. 31.₹252 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹162 (b) ₹90 (c) ₹126 (d) ₹18
32. 32.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 8 days (d) 14 days
33. 33.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 5 days (c) 4 days (d) 6 days
34. 34.If 2 notebooks cost ₹12, how much do 7 notebooks cost? (a) ₹84 (b) ₹17 (c) ₹48 (d) ₹42
35. 35.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 40 days (c) 19 days (d) 7 days
36. 36.₹189 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹81 (b) ₹108 (c) ₹27 (d) ₹135
37. 37.If 3 notebooks cost ₹27, how much do 2 notebooks cost? (a) ₹54 (b) ₹26 (c) ₹18 (d) ₹27
38. 38.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 7 days (c) 52 days (d) 53 days
39. 39.If 4 kites cost ₹88, how much do 7 kites cost? (a) ₹176 (b) ₹616 (c) ₹154 (d) ₹91
40. 40.If 9 notebooks cost ₹180, how much do 11 notebooks cost? (a) ₹182 (b) ₹1980 (c) ₹220 (d) ₹240

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