Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 817 · 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 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 2 days (d) 3 days
2. 2.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 3 days (c) 27 days (d) 15 days
3. 3.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 19 days (c) 7 days (d) 40 days
4. 4.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 28 days (c) 7 days (d) 16 days
5. 5.If 4 kites cost ₹88, how much do 5 kites cost? (a) ₹89 (b) ₹132 (c) ₹440 (d) ₹110
6. 6.If 7 pens cost ₹147, how much do 12 pens cost? (a) ₹273 (b) ₹1764 (c) ₹252 (d) ₹152
7. 7.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 16 days (c) 21 days (d) 20 days
8. 8.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 25 days (d) 9 days
9. 9.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 7 days (d) 6 days
10. 10.If 7 pens cost ₹28, how much do 10 pens cost? (a) ₹44 (b) ₹31 (c) ₹40 (d) ₹280
11. 11.₹416 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹160 (b) ₹208 (c) ₹256 (d) ₹32
12. 12.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 14 days (c) 9 days (d) 8 days
13. 13.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 22 days (d) 21 days
14. 14.If 2 pens cost ₹10, how much do 5 pens cost? (a) ₹13 (b) ₹50 (c) ₹25 (d) ₹30
15. 15.If 7 mangoes cost ₹119, how much do 8 mangoes cost? (a) ₹153 (b) ₹120 (c) ₹136 (d) ₹952
16. 16.If 4 kites cost ₹84, how much do 6 kites cost? (a) ₹147 (b) ₹86 (c) ₹126 (d) ₹504
17. 17.If 5 pens cost ₹100, how much do 12 pens cost? (a) ₹260 (b) ₹1200 (c) ₹107 (d) ₹240
18. 18.If 2 pens cost ₹42, how much do 5 pens cost? (a) ₹126 (b) ₹105 (c) ₹45 (d) ₹210
19. 19.If 7 pens cost ₹119, how much do 9 pens cost? (a) ₹170 (b) ₹1071 (c) ₹153 (d) ₹121
20. 20.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 21 days (c) 9 days (d) 6 days
21. 21.If 5 kites cost ₹125, how much do 2 kites cost? (a) ₹122 (b) ₹250 (c) ₹50 (d) ₹75
22. 22.₹36 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹18 (b) ₹9 (c) ₹36 (d) ₹27
23. 23.If 4 notebooks cost ₹32, how much do 5 notebooks cost? (a) ₹40 (b) ₹33 (c) ₹160 (d) ₹48
24. 24.₹105 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹75 (b) ₹15 (c) ₹60 (d) ₹45
25. 25.If 5 mangoes cost ₹80, how much do 10 mangoes cost? (a) ₹85 (b) ₹800 (c) ₹160 (d) ₹176
26. 26.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 15 days (d) 14 days
27. 27.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 7 days (d) 6 days
28. 28.If 7 notebooks cost ₹147, how much do 3 notebooks cost? (a) ₹84 (b) ₹143 (c) ₹441 (d) ₹63
29. 29.If 5 pens cost ₹50, how much do 6 pens cost? (a) ₹300 (b) ₹60 (c) ₹51 (d) ₹70
30. 30.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 3 days (d) 6 days
31. 31.₹315 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹245 (b) ₹35 (c) ₹280 (d) ₹70
32. 32.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 28 days (c) 27 days (d) 19 days
33. 33.If 8 kites cost ₹144, how much do 10 kites cost? (a) ₹198 (b) ₹146 (c) ₹180 (d) ₹1440
34. 34.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 45 days (b) 7 days (c) 5 days (d) 23 days
35. 35.₹72 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹32 (b) ₹40 (c) ₹36 (d) ₹8
36. 36.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 2 days (c) 18 days (d) 12 days
37. 37.₹261 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹232 (b) ₹261 (c) ₹233 (d) ₹29
38. 38.If 3 notebooks cost ₹66, how much do 4 notebooks cost? (a) ₹110 (b) ₹67 (c) ₹264 (d) ₹88
39. 39.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 11 days (d) 16 days
40. 40.₹234 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹26 (b) ₹117 (c) ₹130 (d) ₹104

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