Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 424 · 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. 1.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 5 days (d) 4 days
2. 2.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 52 days (c) 53 days (d) 19 days
3. 3.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 20 days (c) 4 days (d) 5 days
4. 4.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 9 days (d) 5 days
5. 5.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 24 days (b) 6 days (c) 15 days (d) 9 days
6. 6.If 4 kites cost ₹24, how much do 3 kites cost? (a) ₹24 (b) ₹18 (c) ₹23 (d) ₹72
7. 7.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 11 days (c) 26 days (d) 15 days
8. 8.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 17 days
9. 9.₹187 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹68 (b) ₹17 (c) ₹136 (d) ₹119
10. 10.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 17 days (c) 5 days (d) 44 days
11. 11.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 13 days (d) 4 days
12. 12.₹147 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹63 (b) ₹84 (c) ₹21 (d) ₹105
13. 13.If 6 notebooks cost ₹84, how much do 7 notebooks cost? (a) ₹112 (b) ₹85 (c) ₹98 (d) ₹588
14. 14.If 2 mangoes cost ₹20, how much do 3 mangoes cost? (a) ₹21 (b) ₹60 (c) ₹30 (d) ₹40
15. 15.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 8 days (c) 12 days (d) 3 days
16. 16.If 2 pens cost ₹26, how much do 3 pens cost? (a) ₹27 (b) ₹52 (c) ₹78 (d) ₹39
17. 17.₹231 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹126 (b) ₹21 (c) ₹105 (d) ₹147
18. 18.₹230 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹23 (b) ₹115 (c) ₹161 (d) ₹69
19. 19.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 7 days (d) 5 days
20. 20.₹495 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹45 (b) ₹315 (c) ₹225 (d) ₹270
21. 21.If 7 kites cost ₹119, how much do 9 kites cost? (a) ₹170 (b) ₹121 (c) ₹153 (d) ₹1071
22. 22.₹405 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹180 (b) ₹225 (c) ₹270 (d) ₹45
23. 23.If 4 notebooks cost ₹100, how much do 8 notebooks cost? (a) ₹104 (b) ₹225 (c) ₹200 (d) ₹800
24. 24.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 11 days
25. 25.₹280 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹84 (b) ₹28 (c) ₹140 (d) ₹196
26. 26.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 28 days (c) 3 days (d) 15 days
27. 27.If 5 notebooks cost ₹50, how much do 3 notebooks cost? (a) ₹30 (b) ₹150 (c) ₹48 (d) ₹40
28. 28.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 20 days (b) 6 days (c) 15 days (d) 5 days
29. 29.₹78 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹24 (b) ₹39 (c) ₹6 (d) ₹54
30. 30.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 1 day (c) 16 days (d) 10 days
31. 31.6 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 6 days (d) 14 days
32. 32.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 56 days (b) 20 days (c) 57 days (d) 8 days
33. 33.5 workers can build a wall in 12 days. How many days will 10 workers take, working at the same speed? (a) 24 days (b) 6 days (c) 17 days (d) 7 days
34. 34.₹88 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹77 (b) ₹11 (c) ₹44 (d) ₹88
35. 35.₹49 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹28 (b) ₹7 (c) ₹35 (d) ₹21
36. 36.If 3 pens cost ₹21, how much do 7 pens cost? (a) ₹56 (b) ₹49 (c) ₹25 (d) ₹147
37. 37.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 15 days (d) 14 days
38. 38.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 16 days (c) 14 days (d) 12 days
39. 39.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 2 days (c) 9 days (d) 8 days
40. 40.₹270 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹30 (b) ₹150 (c) ₹120 (d) ₹135

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