Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 40 · 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. 1.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 9 days (d) 8 days
2. 2.₹325 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹125 (b) ₹25 (c) ₹225 (d) ₹200
3. 3.If 2 notebooks cost ₹6, how much do 5 notebooks cost? (a) ₹15 (b) ₹9 (c) ₹18 (d) ₹30
4. 4.₹112 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹42 (b) ₹70 (c) ₹56 (d) ₹14
5. 5.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 7 days (d) 8 days
6. 6.₹180 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹180 (b) ₹90 (c) ₹150 (d) ₹30
7. 7.If 4 mangoes cost ₹36, how much do 9 mangoes cost? (a) ₹90 (b) ₹41 (c) ₹81 (d) ₹324
8. 8.₹60 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹35 (b) ₹30 (c) ₹25 (d) ₹5
9. 9.If 3 kites cost ₹9, how much do 10 kites cost? (a) ₹33 (b) ₹90 (c) ₹30 (d) ₹16
10. 10.₹235 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹188 (b) ₹94 (c) ₹141 (d) ₹47
11. 11.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 22 days (d) 21 days
12. 12.If 3 notebooks cost ₹63, how much do 11 notebooks cost? (a) ₹231 (b) ₹71 (c) ₹693 (d) ₹252
13. 13.If 5 mangoes cost ₹105, how much do 8 mangoes cost? (a) ₹840 (b) ₹108 (c) ₹189 (d) ₹168
14. 14.If 2 pens cost ₹30, how much do 8 pens cost? (a) ₹36 (b) ₹240 (c) ₹135 (d) ₹120
15. 15.₹407 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹37 (b) ₹185 (c) ₹222 (d) ₹259
16. 16.If 6 notebooks cost ₹72, how much do 7 notebooks cost? (a) ₹84 (b) ₹73 (c) ₹504 (d) ₹96
17. 17.If 8 notebooks cost ₹200, how much do 3 notebooks cost? (a) ₹600 (b) ₹195 (c) ₹100 (d) ₹75
18. 18.If 3 pens cost ₹15, how much do 7 pens cost? (a) ₹35 (b) ₹19 (c) ₹40 (d) ₹105
19. 19.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 7 days (d) 2 days
20. 20.If 8 mangoes cost ₹184, how much do 6 mangoes cost? (a) ₹138 (b) ₹1104 (c) ₹182 (d) ₹161
21. 21.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹12 (b) ₹60 (c) ₹108 (d) ₹84
22. 22.If 7 mangoes cost ₹98, how much do 6 mangoes cost? (a) ₹588 (b) ₹84 (c) ₹98 (d) ₹97
23. 23.₹96 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹96 (b) ₹16 (c) ₹80 (d) ₹48
24. 24.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 12 days (d) 5 days
25. 25.₹470 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹47 (b) ₹235 (c) ₹423 (d) ₹470
26. 26.If 8 mangoes cost ₹192, how much do 6 mangoes cost? (a) ₹144 (b) ₹168 (c) ₹1152 (d) ₹190
27. 27.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 6 days (d) 4 days
28. 28.If 3 kites cost ₹57, how much do 4 kites cost? (a) ₹228 (b) ₹95 (c) ₹76 (d) ₹58
29. 29.₹175 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹105 (b) ₹70 (c) ₹35 (d) ₹140
30. 30.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 45 days (b) 9 days (c) 21 days (d) 5 days
31. 31.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 27 days (b) 7 days (c) 17 days (d) 28 days
32. 32.If 3 mangoes cost ₹45, how much do 4 mangoes cost? (a) ₹60 (b) ₹180 (c) ₹75 (d) ₹46
33. 33.If 4 kites cost ₹48, how much do 3 kites cost? (a) ₹47 (b) ₹48 (c) ₹144 (d) ₹36
34. 34.₹105 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹30 (b) ₹90 (c) ₹75 (d) ₹15
35. 35.If 8 kites cost ₹192, how much do 6 kites cost? (a) ₹190 (b) ₹1152 (c) ₹168 (d) ₹144
36. 36.If 6 kites cost ₹48, how much do 3 kites cost? (a) ₹32 (b) ₹144 (c) ₹45 (d) ₹24
37. 37.If 9 pens cost ₹45, how much do 5 pens cost? (a) ₹41 (b) ₹30 (c) ₹225 (d) ₹25
38. 38.₹320 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹40 (b) ₹280 (c) ₹320 (d) ₹160
39. 39.If 5 mangoes cost ₹75, how much do 6 mangoes cost? (a) ₹76 (b) ₹105 (c) ₹90 (d) ₹450
40. 40.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 13 days (c) 9 days (d) 22 days

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