Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 117 · 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.₹500 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹250 (b) ₹50 (c) ₹450 (d) ₹500
2. 2.If 2 pens cost ₹34, how much do 9 pens cost? (a) ₹306 (b) ₹170 (c) ₹153 (d) ₹41
3. 3.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 27 days (d) 26 days
4. 4.If 5 pens cost ₹25, how much do 9 pens cost? (a) ₹45 (b) ₹225 (c) ₹29 (d) ₹50
5. 5.₹385 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹35 (b) ₹70 (c) ₹315 (d) ₹350
6. 6.If 5 notebooks cost ₹115, how much do 4 notebooks cost? (a) ₹115 (b) ₹92 (c) ₹114 (d) ₹460
7. 7.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 17 days (b) 8 days (c) 7 days (d) 6 days
8. 8.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 14 days (b) 5 days (c) 15 days (d) 11 days
9. 9.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 24 days (b) 16 days (c) 6 days (d) 8 days
10. 10.If 2 mangoes cost ₹10, how much do 4 mangoes cost? (a) ₹20 (b) ₹12 (c) ₹25 (d) ₹40
11. 11.If 5 kites cost ₹50, how much do 11 kites cost? (a) ₹120 (b) ₹110 (c) ₹56 (d) ₹550
12. 12.₹98 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹35 (b) ₹63 (c) ₹49 (d) ₹7
13. 13.₹294 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹42 (b) ₹147 (c) ₹294 (d) ₹252
14. 14.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 1 day (c) 16 days (d) 15 days
15. 15.₹117 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹36 (b) ₹90 (c) ₹81 (d) ₹9
16. 16.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 4 days (c) 7 days (d) 3 days
17. 17.If 4 mangoes cost ₹92, how much do 2 mangoes cost? (a) ₹90 (b) ₹184 (c) ₹69 (d) ₹46
18. 18.If 5 kites cost ₹110, how much do 2 kites cost? (a) ₹44 (b) ₹107 (c) ₹66 (d) ₹220
19. 19.₹330 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹165 (b) ₹150 (c) ₹30 (d) ₹180
20. 20.₹144 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹16 (b) ₹64 (c) ₹80 (d) ₹72
21. 21.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 13 days (c) 7 days (d) 25 days
22. 22.If 6 notebooks cost ₹132, how much do 4 notebooks cost? (a) ₹528 (b) ₹110 (c) ₹130 (d) ₹88
23. 23.₹308 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹140 (b) ₹28 (c) ₹168 (d) ₹154
24. 24.₹165 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹165 (b) ₹33 (c) ₹133 (d) ₹132
25. 25.₹187 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹170 (b) ₹153 (c) ₹34 (d) ₹17
26. 26.9 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 19 days (b) 18 days (c) 3 days (d) 13 days
27. 27.If 8 pens cost ₹56, how much do 3 pens cost? (a) ₹51 (b) ₹168 (c) ₹21 (d) ₹28
28. 28.If 4 mangoes cost ₹52, how much do 3 mangoes cost? (a) ₹156 (b) ₹51 (c) ₹39 (d) ₹52
29. 29.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 9 days (c) 22 days (d) 13 days
30. 30.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 5 days (d) 6 days
31. 31.₹132 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹110 (b) ₹66 (c) ₹22 (d) ₹132
32. 32.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 19 days (b) 6 days (c) 18 days (d) 14 days
33. 33.₹24 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹16 (b) ₹12 (c) ₹24 (d) ₹8
34. 34.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 19 days (c) 3 days (d) 2 days
35. 35.If 2 pens cost ₹12, how much do 3 pens cost? (a) ₹36 (b) ₹18 (c) ₹24 (d) ₹13
36. 36.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 1 day (c) 4 days (d) 3 days
37. 37.₹184 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹69 (b) ₹23 (c) ₹115 (d) ₹92
38. 38.₹99 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹9 (b) ₹81 (c) ₹18 (d) ₹90
39. 39.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 3 days (d) 12 days
40. 40.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 21 days (d) 22 days

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