Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 997 · 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.If 3 pens cost ₹24, how much do 6 pens cost? (a) ₹27 (b) ₹56 (c) ₹144 (d) ₹48
2. 2.If 9 notebooks cost ₹189, how much do 4 notebooks cost? (a) ₹84 (b) ₹756 (c) ₹184 (d) ₹105
3. 3.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 28 days (b) 7 days (c) 11 days (d) 17 days
4. 4.₹120 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹108 (b) ₹120 (c) ₹60 (d) ₹12
5. 5.5 workers can build a wall in 12 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 24 days (d) 6 days
6. 6.₹507 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹312 (b) ₹39 (c) ₹351 (d) ₹195
7. 7.If 2 pens cost ₹26, how much do 3 pens cost? (a) ₹52 (b) ₹78 (c) ₹39 (d) ₹27
8. 8.₹234 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹130 (b) ₹117 (c) ₹104 (d) ₹26
9. 9.₹208 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹130 (b) ₹26 (c) ₹104 (d) ₹78
10. 10.₹468 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹234 (b) ₹39 (c) ₹195 (d) ₹273
11. 11.₹376 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹141 (b) ₹47 (c) ₹235 (d) ₹188
12. 12.₹686 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹49 (b) ₹441 (c) ₹245 (d) ₹343
13. 13.7 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
14. 14.If 5 mangoes cost ₹90, how much do 10 mangoes cost? (a) ₹95 (b) ₹900 (c) ₹198 (d) ₹180
15. 15.₹247 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹19 (b) ₹95 (c) ₹152 (d) ₹171
16. 16.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 11 days (d) 3 days
17. 17.₹88 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹66 (b) ₹44 (c) ₹88 (d) ₹22
18. 18.₹171 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹133 (b) ₹152 (c) ₹19 (d) ₹38
19. 19.If 9 pens cost ₹216, how much do 3 pens cost? (a) ₹96 (b) ₹210 (c) ₹648 (d) ₹72
20. 20.If 3 pens cost ₹9, how much do 10 pens cost? (a) ₹90 (b) ₹33 (c) ₹16 (d) ₹30
21. 21.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 7 days (c) 13 days (d) 4 days
22. 22.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 7 days
23. 23.₹351 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹27 (b) ₹243 (c) ₹135 (d) ₹216
24. 24.If 7 pens cost ₹98, how much do 9 pens cost? (a) ₹882 (b) ₹140 (c) ₹100 (d) ₹126
25. 25.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 21 days (c) 22 days (d) 15 days
26. 26.If 7 pens cost ₹112, how much do 11 pens cost? (a) ₹116 (b) ₹1232 (c) ₹176 (d) ₹192
27. 27.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 1 day (c) 22 days (d) 21 days
28. 28.If 3 notebooks cost ₹42, how much do 12 notebooks cost? (a) ₹504 (b) ₹51 (c) ₹182 (d) ₹168
29. 29.If 4 pens cost ₹12, how much do 8 pens cost? (a) ₹16 (b) ₹96 (c) ₹24 (d) ₹27
30. 30.₹550 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹275 (b) ₹150 (c) ₹50 (d) ₹400
31. 31.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 2 days (d) 8 days
32. 32.If 5 mangoes cost ₹25, how much do 12 mangoes cost? (a) ₹32 (b) ₹300 (c) ₹65 (d) ₹60
33. 33.4 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 5 days (d) 11 days
34. 34.If 3 pens cost ₹51, how much do 4 pens cost? (a) ₹204 (b) ₹85 (c) ₹68 (d) ₹52
35. 35.₹63 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹7 (b) ₹56 (c) ₹14 (d) ₹49
36. 36.If 4 notebooks cost ₹72, how much do 3 notebooks cost? (a) ₹72 (b) ₹216 (c) ₹71 (d) ₹54
37. 37.₹128 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹64 (b) ₹128 (c) ₹16 (d) ₹112
38. 38.If 2 kites cost ₹46, how much do 3 kites cost? (a) ₹69 (b) ₹92 (c) ₹47 (d) ₹138
39. 39.If 2 kites cost ₹22, how much do 5 kites cost? (a) ₹66 (b) ₹25 (c) ₹55 (d) ₹110
40. 40.₹110 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹22 (b) ₹55 (c) ₹66 (d) ₹44

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