Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 880 · 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. 1.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 18 days (c) 14 days (d) 19 days
2. 2.If 2 kites cost ₹8, how much do 3 kites cost? (a) ₹24 (b) ₹16 (c) ₹12 (d) ₹9
3. 3.If 5 notebooks cost ₹35, how much do 6 notebooks cost? (a) ₹36 (b) ₹42 (c) ₹49 (d) ₹210
4. 4.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 7 days (c) 4 days (d) 13 days
5. 5.If 7 pens cost ₹126, how much do 2 pens cost? (a) ₹121 (b) ₹36 (c) ₹252 (d) ₹54
6. 6.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 52 days (c) 53 days (d) 7 days
7. 7.₹165 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹135 (b) ₹15 (c) ₹30 (d) ₹150
8. 8.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 5 days (d) 9 days
9. 9.₹210 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹30 (b) ₹105 (c) ₹120 (d) ₹90
10. 10.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 5 days (d) 4 days
11. 11.₹384 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹240 (b) ₹192 (c) ₹144 (d) ₹48
12. 12.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 10 days (c) 3 days (d) 5 days
13. 13.₹154 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹14 (b) ₹98 (c) ₹77 (d) ₹56
14. 14.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹63 (b) ₹7 (c) ₹35 (d) ₹56
15. 15.8 workers can build a wall in 9 days. How many days will 4 workers take, working at the same speed? (a) 18 days (b) 5 days (c) 13 days (d) 19 days
16. 16.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 23 days (c) 22 days (d) 7 days
17. 17.₹72 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹9 (b) ₹45 (c) ₹36 (d) ₹27
18. 18.₹444 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹222 (b) ₹185 (c) ₹259 (d) ₹37
19. 19.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 17 days (d) 25 days
20. 20.9 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 8 days (d) 9 days
21. 21.₹266 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹95 (b) ₹133 (c) ₹171 (d) ₹19
22. 22.₹238 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹34 (b) ₹170 (c) ₹119 (d) ₹68
23. 23.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 17 days (b) 1 day (c) 27 days (d) 3 days
24. 24.₹256 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹128 (b) ₹256 (c) ₹32 (d) ₹224
25. 25.8 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 7 days (d) 9 days
26. 26.If 2 pens cost ₹32, how much do 5 pens cost? (a) ₹35 (b) ₹80 (c) ₹96 (d) ₹160
27. 27.₹65 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹5 (b) ₹25 (c) ₹40 (d) ₹45
28. 28.If 2 notebooks cost ₹34, how much do 7 notebooks cost? (a) ₹238 (b) ₹136 (c) ₹119 (d) ₹39
29. 29.If 5 kites cost ₹95, how much do 12 kites cost? (a) ₹228 (b) ₹1140 (c) ₹102 (d) ₹247
30. 30.₹658 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹235 (b) ₹423 (c) ₹47 (d) ₹329
31. 31.If 4 kites cost ₹52, how much do 7 kites cost? (a) ₹55 (b) ₹104 (c) ₹364 (d) ₹91
32. 32.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 28 days (d) 19 days
33. 33.₹98 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹14 (b) ₹49 (c) ₹98 (d) ₹84
34. 34.₹116 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹58 (b) ₹87 (c) ₹116 (d) ₹29
35. 35.If 3 notebooks cost ₹63, how much do 6 notebooks cost? (a) ₹66 (b) ₹378 (c) ₹147 (d) ₹126
36. 36.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 13 days (b) 4 days (c) 6 days (d) 5 days
37. 37.₹324 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹324 (b) ₹162 (c) ₹36 (d) ₹288
38. 38.If 8 notebooks cost ₹32, how much do 12 notebooks cost? (a) ₹384 (b) ₹48 (c) ₹52 (d) ₹36
39. 39.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 25 days (d) 16 days
40. 40.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 10 days (c) 14 days (d) 15 days

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