Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 423 · 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.₹350 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹125 (b) ₹225 (c) ₹25 (d) ₹175
2. 2.₹189 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹147 (b) ₹21 (c) ₹168 (d) ₹42
3. 3.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 7 days (d) 5 days
4. 4.If 3 mangoes cost ₹57, how much do 11 mangoes cost? (a) ₹65 (b) ₹627 (c) ₹228 (d) ₹209
5. 5.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 3 days (d) 8 days
6. 6.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 3 days (c) 4 days (d) 8 days
7. 7.If 9 pens cost ₹180, how much do 6 pens cost? (a) ₹1080 (b) ₹120 (c) ₹177 (d) ₹140
8. 8.₹585 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹405 (b) ₹450 (c) ₹180 (d) ₹45
9. 9.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 13 days (c) 26 days (d) 27 days
10. 10.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 8 days (d) 2 days
11. 11.₹45 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹15 (b) ₹30 (c) ₹31 (d) ₹45
12. 12.₹297 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹54 (b) ₹243 (c) ₹270 (d) ₹27
13. 13.₹153 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹85 (b) ₹17 (c) ₹102 (d) ₹68
14. 14.₹279 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹186 (b) ₹31 (c) ₹155 (d) ₹124
15. 15.If 2 notebooks cost ₹10, how much do 3 notebooks cost? (a) ₹20 (b) ₹11 (c) ₹15 (d) ₹30
16. 16.₹312 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹120 (b) ₹156 (c) ₹24 (d) ₹192
17. 17.₹126 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹9 (b) ₹63 (c) ₹45 (d) ₹81
18. 18.₹132 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹12 (b) ₹66 (c) ₹48 (d) ₹84
19. 19.If 2 mangoes cost ₹26, how much do 5 mangoes cost? (a) ₹65 (b) ₹78 (c) ₹130 (d) ₹29
20. 20.3 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) 3 days (d) 4 days
21. 21.If 6 pens cost ₹150, how much do 9 pens cost? (a) ₹153 (b) ₹250 (c) ₹225 (d) ₹1350
22. 22.₹153 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹17 (b) ₹153 (c) ₹136 (d) ₹137
23. 23.If 5 kites cost ₹75, how much do 3 kites cost? (a) ₹225 (b) ₹60 (c) ₹45 (d) ₹73
24. 24.If 4 pens cost ₹16, how much do 12 pens cost? (a) ₹24 (b) ₹52 (c) ₹48 (d) ₹192
25. 25.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 9 days (c) 3 days (d) 15 days
26. 26.₹644 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹414 (b) ₹322 (c) ₹46 (d) ₹230
27. 27.If 3 notebooks cost ₹24, how much do 6 notebooks cost? (a) ₹48 (b) ₹144 (c) ₹56 (d) ₹27
28. 28.₹64 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹32 (b) ₹16 (c) ₹64 (d) ₹48
29. 29.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 28 days (b) 17 days (c) 11 days (d) 7 days
30. 30.₹377 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹290 (b) ₹29 (c) ₹116 (d) ₹261
31. 31.₹108 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹108 (b) ₹90 (c) ₹18 (d) ₹54
32. 32.If 4 pens cost ₹96, how much do 5 pens cost? (a) ₹480 (b) ₹97 (c) ₹144 (d) ₹120
33. 33.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 13 days (b) 6 days (c) 5 days (d) 4 days
34. 34.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 11 days (c) 19 days (d) 7 days
35. 35.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 21 days (b) 9 days (c) 5 days (d) 45 days
36. 36.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 49 days (c) 9 days (d) 4 days
37. 37.If 5 notebooks cost ₹85, how much do 12 notebooks cost? (a) ₹204 (b) ₹1020 (c) ₹92 (d) ₹221
38. 38.₹60 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹10 (b) ₹30 (c) ₹60 (d) ₹50
39. 39.₹410 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹410 (b) ₹205 (c) ₹369 (d) ₹41
40. 40.If 9 pens cost ₹207, how much do 10 pens cost? (a) ₹2070 (b) ₹230 (c) ₹208 (d) ₹253

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