Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 528 · 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. 1.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 14 days (c) 11 days (d) 15 days
2. 2.₹279 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹124 (b) ₹186 (c) ₹31 (d) ₹155
3. 3.If 8 kites cost ₹104, how much do 9 kites cost? (a) ₹117 (b) ₹130 (c) ₹936 (d) ₹105
4. 4.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 20 days (d) 21 days
5. 5.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 23 days (c) 13 days (d) 22 days
6. 6.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 26 days (b) 27 days (c) 17 days (d) 9 days
7. 7.₹80 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹40 (b) ₹64 (c) ₹16 (d) ₹80
8. 8.If 5 mangoes cost ₹15, how much do 12 mangoes cost? (a) ₹22 (b) ₹39 (c) ₹36 (d) ₹180
9. 9.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 4 days (d) 10 days
10. 10.If 5 kites cost ₹125, how much do 7 kites cost? (a) ₹200 (b) ₹127 (c) ₹875 (d) ₹175
11. 11.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 4 days (c) 5 days (d) 6 days
12. 12.₹234 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹117 (b) ₹26 (c) ₹52 (d) ₹182
13. 13.If 8 pens cost ₹72, how much do 12 pens cost? (a) ₹76 (b) ₹864 (c) ₹117 (d) ₹108
14. 14.If 8 mangoes cost ₹32, how much do 7 mangoes cost? (a) ₹31 (b) ₹224 (c) ₹28 (d) ₹32
15. 15.If 3 kites cost ₹39, how much do 11 kites cost? (a) ₹47 (b) ₹143 (c) ₹429 (d) ₹156
16. 16.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 19 days (c) 4 days (d) 3 days
17. 17.₹456 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹228 (b) ₹38 (c) ₹266 (d) ₹190
18. 18.₹315 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹140 (b) ₹175 (c) ₹210 (d) ₹35
19. 19.If 9 pens cost ₹63, how much do 7 pens cost? (a) ₹56 (b) ₹441 (c) ₹49 (d) ₹61
20. 20.₹77 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹44 (b) ₹55 (c) ₹11 (d) ₹33
21. 21.₹495 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹315 (b) ₹45 (c) ₹270 (d) ₹225
22. 22.If 6 kites cost ₹108, how much do 8 kites cost? (a) ₹864 (b) ₹162 (c) ₹110 (d) ₹144
23. 23.3 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) 3 days (d) 2 days
24. 24.If 9 notebooks cost ₹171, how much do 7 notebooks cost? (a) ₹133 (b) ₹152 (c) ₹169 (d) ₹1197
25. 25.₹450 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹400 (b) ₹225 (c) ₹50 (d) ₹450
26. 26.If 4 kites cost ₹68, how much do 5 kites cost? (a) ₹102 (b) ₹69 (c) ₹85 (d) ₹340
27. 27.₹252 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹126 (b) ₹90 (c) ₹18 (d) ₹162
28. 28.If 7 kites cost ₹84, how much do 9 kites cost? (a) ₹120 (b) ₹86 (c) ₹756 (d) ₹108
29. 29.8 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) 44 days (d) 5 days
30. 30.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 20 days (b) 5 days (c) 6 days (d) 15 days
31. 31.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 2 days (d) 1 day
32. 32.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 17 days (c) 16 days (d) 12 days
33. 33.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 9 days (d) 12 days
34. 34.₹378 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹189 (b) ₹378 (c) ₹336 (d) ₹42
35. 35.₹132 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹96 (b) ₹36 (c) ₹12 (d) ₹66
36. 36.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 16 days (b) 17 days (c) 7 days (d) 13 days
37. 37.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 11 days (d) 13 days
38. 38.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 7 days (c) 23 days (d) 22 days
39. 39.₹440 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹40 (b) ₹220 (c) ₹160 (d) ₹280
40. 40.If 5 kites cost ₹45, how much do 8 kites cost? (a) ₹48 (b) ₹360 (c) ₹81 (d) ₹72

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