Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 237 · 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. 1.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 10 days (c) 6 days (d) 7 days
2. 2.If 9 notebooks cost ₹99, how much do 10 notebooks cost? (a) ₹121 (b) ₹990 (c) ₹100 (d) ₹110
3. 3.If 2 kites cost ₹24, how much do 7 kites cost? (a) ₹96 (b) ₹29 (c) ₹84 (d) ₹168
4. 4.If 8 kites cost ₹144, how much do 3 kites cost? (a) ₹72 (b) ₹139 (c) ₹432 (d) ₹54
5. 5.If 8 pens cost ₹56, how much do 10 pens cost? (a) ₹70 (b) ₹58 (c) ₹77 (d) ₹560
6. 6.₹423 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹235 (b) ₹188 (c) ₹47 (d) ₹282
7. 7.If 2 pens cost ₹46, how much do 10 pens cost? (a) ₹54 (b) ₹460 (c) ₹253 (d) ₹230
8. 8.₹115 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹93 (b) ₹115 (c) ₹92 (d) ₹23
9. 9.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 14 days (c) 5 days (d) 15 days
10. 10.If 2 pens cost ₹24, how much do 10 pens cost? (a) ₹240 (b) ₹32 (c) ₹120 (d) ₹132
11. 11.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 20 days (b) 7 days (c) 5 days (d) 13 days
12. 12.₹385 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹175 (b) ₹35 (c) ₹210 (d) ₹245
13. 13.If 7 mangoes cost ₹35, how much do 2 mangoes cost? (a) ₹70 (b) ₹30 (c) ₹15 (d) ₹10
14. 14.₹221 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹136 (b) ₹17 (c) ₹153 (d) ₹85
15. 15.₹32 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹16 (b) ₹32 (c) ₹8 (d) ₹24
16. 16.If 7 mangoes cost ₹28, how much do 10 mangoes cost? (a) ₹44 (b) ₹280 (c) ₹31 (d) ₹40
17. 17.If 4 pens cost ₹88, how much do 12 pens cost? (a) ₹1056 (b) ₹286 (c) ₹264 (d) ₹96
18. 18.If 5 mangoes cost ₹105, how much do 2 mangoes cost? (a) ₹210 (b) ₹63 (c) ₹102 (d) ₹42
19. 19.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 14 days (c) 4 days (d) 5 days
20. 20.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 19 days (d) 2 days
21. 21.If 6 notebooks cost ₹84, how much do 5 notebooks cost? (a) ₹84 (b) ₹83 (c) ₹420 (d) ₹70
22. 22.₹140 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹70 (b) ₹42 (c) ₹14 (d) ₹98
23. 23.If 7 kites cost ₹91, how much do 10 kites cost? (a) ₹94 (b) ₹143 (c) ₹130 (d) ₹910
24. 24.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 26 days (b) 27 days (c) 10 days (d) 16 days
25. 25.If 8 pens cost ₹64, how much do 2 pens cost? (a) ₹16 (b) ₹58 (c) ₹24 (d) ₹128
26. 26.₹120 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹60 (b) ₹24 (c) ₹96 (d) ₹120
27. 27.If 7 mangoes cost ₹105, how much do 4 mangoes cost? (a) ₹102 (b) ₹420 (c) ₹60 (d) ₹75
28. 28.If 2 notebooks cost ₹50, how much do 6 notebooks cost? (a) ₹175 (b) ₹300 (c) ₹150 (d) ₹54
29. 29.₹165 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹60 (b) ₹120 (c) ₹105 (d) ₹15
30. 30.₹117 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹65 (b) ₹13 (c) ₹78 (d) ₹52
31. 31.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 3 days (d) 2 days
32. 32.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 1 day (b) 2 days (c) 8 days (d) 3 days
33. 33.If 6 pens cost ₹144, how much do 4 pens cost? (a) ₹142 (b) ₹96 (c) ₹576 (d) ₹120
34. 34.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹119 (b) ₹102 (c) ₹85 (d) ₹17
35. 35.₹490 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹245 (b) ₹441 (c) ₹490 (d) ₹49
36. 36.If 2 pens cost ₹6, how much do 3 pens cost? (a) ₹9 (b) ₹7 (c) ₹18 (d) ₹12
37. 37.₹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
38. 38.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 17 days (c) 4 days (d) 16 days
39. 39.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 14 days (d) 9 days
40. 40.₹342 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹171 (b) ₹152 (c) ₹38 (d) ₹190

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