Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 677 · 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 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 2 days (d) 4 days
2. 2.5 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 14 days (c) 20 days (d) 21 days
3. 3.₹88 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹11 (b) ₹55 (c) ₹33 (d) ₹44
4. 4.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 28 days (c) 15 days (d) 27 days
5. 5.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 28 days (c) 18 days (d) 7 days
6. 6.₹85 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹68 (b) ₹34 (c) ₹17 (d) ₹51
7. 7.9 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 8 days (d) 9 days
8. 8.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 12 days (c) 8 days (d) 20 days
9. 9.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 21 days (c) 13 days (d) 22 days
10. 10.If 3 notebooks cost ₹45, how much do 4 notebooks cost? (a) ₹180 (b) ₹60 (c) ₹75 (d) ₹46
11. 11.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 18 days (d) 14 days
12. 12.₹280 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹175 (b) ₹140 (c) ₹35 (d) ₹105
13. 13.₹240 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹120 (b) ₹240 (c) ₹210 (d) ₹30
14. 14.₹270 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹81 (b) ₹135 (c) ₹27 (d) ₹189
15. 15.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 7 days (d) 15 days
16. 16.If 6 kites cost ₹78, how much do 4 kites cost? (a) ₹65 (b) ₹76 (c) ₹52 (d) ₹312
17. 17.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 9 days (d) 10 days
18. 18.If 8 pens cost ₹64, how much do 12 pens cost? (a) ₹768 (b) ₹68 (c) ₹104 (d) ₹96
19. 19.₹117 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹91 (b) ₹26 (c) ₹104 (d) ₹13
20. 20.If 8 pens cost ₹24, how much do 6 pens cost? (a) ₹22 (b) ₹144 (c) ₹18 (d) ₹21
21. 21.₹64 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹8 (b) ₹64 (c) ₹32 (d) ₹56
22. 22.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 30 days (c) 31 days (d) 18 days
23. 23.₹21 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹7 (b) ₹14 (c) ₹21 (d) ₹15
24. 24.If 4 notebooks cost ₹20, how much do 5 notebooks cost? (a) ₹100 (b) ₹30 (c) ₹25 (d) ₹21
25. 25.If 2 mangoes cost ₹16, how much do 12 mangoes cost? (a) ₹96 (b) ₹192 (c) ₹104 (d) ₹26
26. 26.If 9 kites cost ₹144, how much do 6 kites cost? (a) ₹96 (b) ₹864 (c) ₹141 (d) ₹112
27. 27.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 13 days (b) 6 days (c) 5 days (d) 4 days
28. 28.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 24 days (c) 6 days (d) 15 days
29. 29.9 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 3 days (c) 45 days (d) 46 days
30. 30.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 45 days (c) 9 days (d) 5 days
31. 31.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 6 days (b) 24 days (c) 15 days (d) 9 days
32. 32.If 4 mangoes cost ₹48, how much do 6 mangoes cost? (a) ₹288 (b) ₹72 (c) ₹84 (d) ₹50
33. 33.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 3 days (d) 7 days
34. 34.If 9 pens cost ₹144, how much do 11 pens cost? (a) ₹192 (b) ₹176 (c) ₹146 (d) ₹1584
35. 35.₹84 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹56 (b) ₹84 (c) ₹28 (d) ₹42
36. 36.If 8 pens cost ₹64, how much do 10 pens cost? (a) ₹66 (b) ₹640 (c) ₹80 (d) ₹88
37. 37.₹63 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹36 (b) ₹27 (c) ₹45 (d) ₹9
38. 38.₹550 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹50 (b) ₹450 (c) ₹100 (d) ₹275
39. 39.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 42 days (b) 43 days (c) 8 days (d) 20 days
40. 40.If 4 mangoes cost ₹32, how much do 3 mangoes cost? (a) ₹31 (b) ₹32 (c) ₹24 (d) ₹96

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