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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 435 · 40 questions
TalentJR

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.

NameDateTime takenScore ___ / 40
  1. 1.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 13 days (b) 4 days (c) 2 days (d) 3 days
  2. 2.If 8 mangoes cost ₹32, how much do 2 mangoes cost? (a) ₹26 (b) ₹64 (c) ₹8 (d) ₹12
  3. 3.₹598 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹299 (b) ₹368 (c) ₹46 (d) ₹230
  4. 4.₹52 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹52 (b) ₹26 (c) ₹13 (d) ₹39
  5. 5.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 16 days (b) 5 days (c) 25 days (d) 4 days
  6. 6.If 3 notebooks cost ₹72, how much do 7 notebooks cost? (a) ₹192 (b) ₹504 (c) ₹168 (d) ₹76
  7. 7.₹315 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹280 (b) ₹70 (c) ₹35 (d) ₹245
  8. 8.If 5 kites cost ₹30, how much do 2 kites cost? (a) ₹60 (b) ₹12 (c) ₹18 (d) ₹27
  9. 9.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 10 days (d) 5 days
  10. 10.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 54 days (b) 19 days (c) 55 days (d) 5 days
  11. 11.₹329 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹47 (b) ₹235 (c) ₹282 (d) ₹94
  12. 12.If 6 kites cost ₹90, how much do 7 kites cost? (a) ₹630 (b) ₹105 (c) ₹91 (d) ₹120
  13. 13.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 8 days (d) 1 day
  14. 14.₹156 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹39 (b) ₹156 (c) ₹117 (d) ₹78
  15. 15.If 8 mangoes cost ₹64, how much do 11 mangoes cost? (a) ₹67 (b) ₹704 (c) ₹96 (d) ₹88
  16. 16.If 2 notebooks cost ₹16, how much do 9 notebooks cost? (a) ₹23 (b) ₹144 (c) ₹80 (d) ₹72
  17. 17.If 8 notebooks cost ₹160, how much do 4 notebooks cost? (a) ₹640 (b) ₹100 (c) ₹80 (d) ₹156
  18. 18.If 9 mangoes cost ₹45, how much do 12 mangoes cost? (a) ₹65 (b) ₹48 (c) ₹60 (d) ₹540
  19. 19.₹275 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹100 (b) ₹200 (c) ₹175 (d) ₹25
  20. 20.₹133 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹19 (b) ₹95 (c) ₹38 (d) ₹114
  21. 21.If 2 kites cost ₹18, how much do 8 kites cost? (a) ₹144 (b) ₹72 (c) ₹81 (d) ₹24
  22. 22.₹387 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹43 (b) ₹172 (c) ₹215 (d) ₹258
  23. 23.If 4 mangoes cost ₹32, how much do 5 mangoes cost? (a) ₹40 (b) ₹48 (c) ₹33 (d) ₹160
  24. 24.₹245 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹98 (b) ₹147 (c) ₹196 (d) ₹49
  25. 25.If 3 notebooks cost ₹27, how much do 4 notebooks cost? (a) ₹28 (b) ₹45 (c) ₹108 (d) ₹36
  26. 26.If 3 kites cost ₹9, how much do 11 kites cost? (a) ₹99 (b) ₹33 (c) ₹36 (d) ₹17
  27. 27.If 4 pens cost ₹44, how much do 5 pens cost? (a) ₹45 (b) ₹55 (c) ₹66 (d) ₹220
  28. 28.₹132 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹60 (b) ₹12 (c) ₹72 (d) ₹66
  29. 29.₹80 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹32 (b) ₹16 (c) ₹48 (d) ₹40
  30. 30.If 7 notebooks cost ₹21, how much do 8 notebooks cost? (a) ₹22 (b) ₹24 (c) ₹27 (d) ₹168
  31. 31.₹35 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹25 (b) ₹30 (c) ₹5 (d) ₹10
  32. 32.₹70 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹35 (b) ₹30 (c) ₹10 (d) ₹40
  33. 33.If 8 kites cost ₹184, how much do 2 kites cost? (a) ₹69 (b) ₹368 (c) ₹178 (d) ₹46
  34. 34.If 3 kites cost ₹39, how much do 6 kites cost? (a) ₹234 (b) ₹91 (c) ₹78 (d) ₹42
  35. 35.If 2 kites cost ₹36, how much do 12 kites cost? (a) ₹46 (b) ₹432 (c) ₹234 (d) ₹216
  36. 36.If 2 mangoes cost ₹46, how much do 11 mangoes cost? (a) ₹55 (b) ₹276 (c) ₹506 (d) ₹253
  37. 37.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 57 days (c) 20 days (d) 56 days
  38. 38.₹140 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹80 (b) ₹70 (c) ₹20 (d) ₹60
  39. 39.₹35 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹29 (b) ₹7 (c) ₹35 (d) ₹28
  40. 40.If 2 notebooks cost ₹18, how much do 10 notebooks cost? (a) ₹90 (b) ₹26 (c) ₹99 (d) ₹180

Answer key

  1. 3 days
  2. ₹8
  3. ₹368
  4. ₹39
  5. 4 days
  6. ₹168
  7. ₹245
  8. ₹12
  9. 9 days
  10. 54 days
  11. ₹235
  12. ₹105
  13. 2 days
  14. ₹117
  15. ₹88
  16. ₹72
  17. ₹80
  18. ₹60
  19. ₹175
  20. ₹95
  21. ₹72
  22. ₹215
  23. ₹40
  24. ₹147
  25. ₹36
  26. ₹33
  27. ₹55
  28. ₹72
  29. ₹48
  30. ₹24
  31. ₹25
  32. ₹40
  33. ₹46
  34. ₹78
  35. ₹216
  36. ₹253
  37. 56 days
  38. ₹80
  39. ₹28
  40. ₹90

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