Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 404 · 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 8 mangoes cost ₹200, how much do 12 mangoes cost? (a) ₹300 (b) ₹2400 (c) ₹204 (d) ₹325
2. 2.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 11 days (d) 3 days
3. 3.If 5 notebooks cost ₹100, how much do 8 notebooks cost? (a) ₹103 (b) ₹800 (c) ₹160 (d) ₹180
4. 4.₹165 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹66 (b) ₹33 (c) ₹132 (d) ₹99
5. 5.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 13 days (b) 16 days (c) 3 days (d) 4 days
6. 6.₹198 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹22 (b) ₹176 (c) ₹99 (d) ₹198
7. 7.If 7 kites cost ₹112, how much do 9 kites cost? (a) ₹160 (b) ₹114 (c) ₹1008 (d) ₹144
8. 8.If 3 pens cost ₹66, how much do 7 pens cost? (a) ₹154 (b) ₹176 (c) ₹462 (d) ₹70
9. 9.₹77 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹33 (b) ₹55 (c) ₹44 (d) ₹11
10. 10.₹390 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹39 (b) ₹390 (c) ₹351 (d) ₹195
11. 11.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 36 days (d) 18 days
12. 12.8 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) 8 days (d) 7 days
13. 13.₹88 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹55 (b) ₹44 (c) ₹33 (d) ₹11
14. 14.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 13 days (c) 16 days (d) 9 days
15. 15.If 2 kites cost ₹18, how much do 8 kites cost? (a) ₹24 (b) ₹72 (c) ₹144 (d) ₹81
16. 16.₹235 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹235 (b) ₹188 (c) ₹47 (d) ₹189
17. 17.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 26 days (c) 11 days (d) 27 days
18. 18.₹341 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹248 (b) ₹31 (c) ₹217 (d) ₹124
19. 19.₹128 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹64 (b) ₹112 (c) ₹16 (d) ₹128
20. 20.If 4 pens cost ₹32, how much do 8 pens cost? (a) ₹256 (b) ₹36 (c) ₹72 (d) ₹64
21. 21.₹104 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹39 (b) ₹52 (c) ₹13 (d) ₹65
22. 22.₹352 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹176 (b) ₹32 (c) ₹256 (d) ₹96
23. 23.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 13 days (c) 7 days (d) 4 days
24. 24.If 5 pens cost ₹110, how much do 9 pens cost? (a) ₹220 (b) ₹114 (c) ₹198 (d) ₹990
25. 25.If 3 pens cost ₹9, how much do 10 pens cost? (a) ₹16 (b) ₹33 (c) ₹90 (d) ₹30
26. 26.₹304 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹38 (b) ₹114 (c) ₹152 (d) ₹190
27. 27.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 15 days (c) 4 days (d) 10 days
28. 28.₹279 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹31 (b) ₹186 (c) ₹155 (d) ₹124
29. 29.₹153 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹119 (b) ₹34 (c) ₹136 (d) ₹17
30. 30.If 8 pens cost ₹24, how much do 3 pens cost? (a) ₹19 (b) ₹9 (c) ₹72 (d) ₹12
31. 31.If 8 notebooks cost ₹48, how much do 5 notebooks cost? (a) ₹45 (b) ₹240 (c) ₹36 (d) ₹30
32. 32.₹161 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹92 (b) ₹23 (c) ₹69 (d) ₹115
33. 33.If 5 mangoes cost ₹55, how much do 3 mangoes cost? (a) ₹53 (b) ₹44 (c) ₹33 (d) ₹165
34. 34.8 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 8 days (d) 7 days
35. 35.₹65 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹45 (b) ₹40 (c) ₹5 (d) ₹25
36. 36.If 4 pens cost ₹100, how much do 9 pens cost? (a) ₹105 (b) ₹900 (c) ₹225 (d) ₹250
37. 37.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 13 days (c) 16 days (d) 15 days
38. 38.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 9 days (d) 24 days
39. 39.If 4 pens cost ₹40, how much do 6 pens cost? (a) ₹42 (b) ₹70 (c) ₹240 (d) ₹60
40. 40.₹351 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹39 (b) ₹351 (c) ₹313 (d) ₹312

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