Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 539 · 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 6 pens cost ₹24, how much do 8 pens cost? (a) ₹32 (b) ₹26 (c) ₹36 (d) ₹192
2. 2.If 2 mangoes cost ₹26, how much do 5 mangoes cost? (a) ₹29 (b) ₹65 (c) ₹130 (d) ₹78
3. 3.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 3 days (d) 5 days
4. 4.If 8 mangoes cost ₹192, how much do 11 mangoes cost? (a) ₹195 (b) ₹288 (c) ₹264 (d) ₹2112
5. 5.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 9 days (c) 7 days (d) 8 days
6. 6.₹60 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹10 (b) ₹60 (c) ₹50 (d) ₹30
7. 7.If 5 notebooks cost ₹115, how much do 9 notebooks cost? (a) ₹230 (b) ₹207 (c) ₹119 (d) ₹1035
8. 8.₹171 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹38 (b) ₹19 (c) ₹133 (d) ₹152
9. 9.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 26 days (c) 15 days (d) 27 days
10. 10.If 8 notebooks cost ₹56, how much do 3 notebooks cost? (a) ₹21 (b) ₹168 (c) ₹51 (d) ₹28
11. 11.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 30 days (c) 31 days (d) 17 days
12. 12.₹84 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹42 (b) ₹30 (c) ₹6 (d) ₹54
13. 13.₹272 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹34 (b) ₹136 (c) ₹272 (d) ₹238
14. 14.₹385 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹175 (b) ₹210 (c) ₹35 (d) ₹245
15. 15.If 2 kites cost ₹12, how much do 12 kites cost? (a) ₹78 (b) ₹144 (c) ₹22 (d) ₹72
16. 16.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹35 (b) ₹63 (c) ₹56 (d) ₹7
17. 17.If 4 notebooks cost ₹88, how much do 5 notebooks cost? (a) ₹440 (b) ₹89 (c) ₹110 (d) ₹132
18. 18.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 17 days (d) 4 days
19. 19.₹588 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹42 (b) ₹294 (c) ₹378 (d) ₹210
20. 20.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 15 days (d) 14 days
21. 21.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 3 days (d) 5 days
22. 22.₹104 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹104 (b) ₹78 (c) ₹52 (d) ₹26
23. 23.₹54 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹36 (b) ₹54 (c) ₹27 (d) ₹18
24. 24.If 2 notebooks cost ₹30, how much do 7 notebooks cost? (a) ₹120 (b) ₹210 (c) ₹105 (d) ₹35
25. 25.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 25 days (d) 13 days
26. 26.₹312 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹39 (b) ₹195 (c) ₹117 (d) ₹156
27. 27.₹216 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹81 (b) ₹108 (c) ₹135 (d) ₹27
28. 28.₹418 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹38 (b) ₹228 (c) ₹209 (d) ₹190
29. 29.₹341 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹217 (b) ₹186 (c) ₹31 (d) ₹155
30. 30.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 13 days (d) 9 days
31. 31.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 14 days (c) 8 days (d) 15 days
32. 32.₹574 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹41 (b) ₹369 (c) ₹205 (d) ₹287
33. 33.If 5 mangoes cost ₹120, how much do 4 mangoes cost? (a) ₹480 (b) ₹120 (c) ₹96 (d) ₹119
34. 34.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 28 days (b) 7 days (c) 18 days (d) 10 days
35. 35.If 9 notebooks cost ₹207, how much do 6 notebooks cost? (a) ₹161 (b) ₹1242 (c) ₹138 (d) ₹204
36. 36.If 7 mangoes cost ₹154, how much do 8 mangoes cost? (a) ₹155 (b) ₹176 (c) ₹1232 (d) ₹198
37. 37.₹66 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹33 (b) ₹6 (c) ₹18 (d) ₹48
38. 38.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 9 days (c) 15 days (d) 16 days
39. 39.₹154 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹98 (b) ₹14 (c) ₹56 (d) ₹77
40. 40.₹315 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹175 (b) ₹35 (c) ₹210 (d) ₹140

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