Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 558 · 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. 1.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 5 days (c) 12 days (d) 4 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) 27 days (c) 15 days (d) 3 days
3. 3.If 2 kites cost ₹24, how much do 3 kites cost? (a) ₹72 (b) ₹25 (c) ₹48 (d) ₹36
4. 4.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 43 days (c) 42 days (d) 8 days
5. 5.₹320 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹224 (b) ₹160 (c) ₹96 (d) ₹32
6. 6.If 8 mangoes cost ₹96, how much do 6 mangoes cost? (a) ₹84 (b) ₹72 (c) ₹576 (d) ₹94
7. 7.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 27 days (b) 28 days (c) 11 days (d) 19 days
8. 8.₹279 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹31 (b) ₹186 (c) ₹155 (d) ₹124
9. 9.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 15 days (d) 16 days
10. 10.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 19 days (d) 18 days
11. 11.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 17 days (d) 16 days
12. 12.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 7 days (c) 16 days (d) 13 days
13. 13.₹130 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹26 (b) ₹130 (c) ₹104 (d) ₹65
14. 14.₹216 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹27 (b) ₹108 (c) ₹81 (d) ₹135
15. 15.If 2 pens cost ₹42, how much do 5 pens cost? (a) ₹210 (b) ₹105 (c) ₹126 (d) ₹45
16. 16.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 7 days
17. 17.₹280 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹140 (b) ₹245 (c) ₹35 (d) ₹280
18. 18.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 7 days (c) 28 days (d) 12 days
19. 19.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 14 days (c) 9 days (d) 15 days
20. 20.If 9 pens cost ₹198, how much do 5 pens cost? (a) ₹194 (b) ₹132 (c) ₹990 (d) ₹110
21. 21.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 13 days (d) 6 days
22. 22.6 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 30 days (b) 31 days (c) 14 days (d) 6 days
23. 23.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 3 days (d) 4 days
24. 24.If 4 notebooks cost ₹48, how much do 9 notebooks cost? (a) ₹53 (b) ₹120 (c) ₹432 (d) ₹108
25. 25.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 6 days (d) 7 days
26. 26.₹252 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹105 (b) ₹126 (c) ₹147 (d) ₹21
27. 27.₹440 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹220 (b) ₹440 (c) ₹44 (d) ₹396
28. 28.₹128 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹128 (b) ₹64 (c) ₹112 (d) ₹16
29. 29.₹352 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹96 (b) ₹256 (c) ₹176 (d) ₹32
30. 30.If 3 notebooks cost ₹24, how much do 11 notebooks cost? (a) ₹264 (b) ₹88 (c) ₹96 (d) ₹32
31. 31.If 5 notebooks cost ₹110, how much do 9 notebooks cost? (a) ₹114 (b) ₹990 (c) ₹198 (d) ₹220
32. 32.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 26 days (d) 13 days
33. 33.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 1 day (d) 4 days
34. 34.₹304 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹38 (b) ₹266 (c) ₹304 (d) ₹152
35. 35.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 13 days (d) 1 day
36. 36.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 1 day (c) 11 days (d) 3 days
37. 37.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 6 days (d) 4 days
38. 38.6 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 4 days (c) 8 days (d) 16 days
39. 39.₹341 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹217 (b) ₹124 (c) ₹31 (d) ₹248
40. 40.If 8 mangoes cost ₹176, how much do 4 mangoes cost? (a) ₹704 (b) ₹110 (c) ₹172 (d) ₹88

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