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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 79 · 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. 1.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 10 days (d) 6 days
  2. 2.If 3 notebooks cost ₹30, how much do 10 notebooks cost? (a) ₹37 (b) ₹110 (c) ₹300 (d) ₹100
  3. 3.If 5 mangoes cost ₹80, how much do 2 mangoes cost? (a) ₹48 (b) ₹32 (c) ₹77 (d) ₹160
  4. 4.₹585 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹180 (b) ₹450 (c) ₹45 (d) ₹405
  5. 5.₹368 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹46 (b) ₹368 (c) ₹184 (d) ₹322
  6. 6.₹99 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹9 (b) ₹18 (c) ₹81 (d) ₹90
  7. 7.If 5 kites cost ₹20, how much do 2 kites cost? (a) ₹12 (b) ₹40 (c) ₹8 (d) ₹17
  8. 8.₹273 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹39 (b) ₹156 (c) ₹195 (d) ₹117
  9. 9.If 4 pens cost ₹20, how much do 2 pens cost? (a) ₹15 (b) ₹18 (c) ₹40 (d) ₹10
  10. 10.₹56 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹28 (b) ₹14 (c) ₹42 (d) ₹56
  11. 11.If 5 notebooks cost ₹35, how much do 11 notebooks cost? (a) ₹385 (b) ₹41 (c) ₹84 (d) ₹77
  12. 12.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 8 days (d) 11 days
  13. 13.₹125 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹100 (b) ₹25 (c) ₹125 (d) ₹101
  14. 14.If 3 kites cost ₹42, how much do 8 kites cost? (a) ₹336 (b) ₹126 (c) ₹47 (d) ₹112
  15. 15.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 18 days (b) 14 days (c) 2 days (d) 3 days
  16. 16.₹378 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹27 (b) ₹135 (c) ₹243 (d) ₹189
  17. 17.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 17 days (b) 11 days (c) 21 days (d) 22 days
  18. 18.If 5 notebooks cost ₹25, how much do 12 notebooks cost? (a) ₹65 (b) ₹300 (c) ₹32 (d) ₹60
  19. 19.If 9 kites cost ₹189, how much do 10 kites cost? (a) ₹1890 (b) ₹190 (c) ₹231 (d) ₹210
  20. 20.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 15 days (d) 16 days
  21. 21.If 7 notebooks cost ₹21, how much do 2 notebooks cost? (a) ₹42 (b) ₹6 (c) ₹16 (d) ₹9
  22. 22.₹242 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹121 (b) ₹132 (c) ₹110 (d) ₹22
  23. 23.If 6 pens cost ₹138, how much do 7 pens cost? (a) ₹966 (b) ₹161 (c) ₹139 (d) ₹184
  24. 24.₹352 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹176 (b) ₹352 (c) ₹44 (d) ₹308
  25. 25.If 8 notebooks cost ₹56, how much do 3 notebooks cost? (a) ₹51 (b) ₹28 (c) ₹21 (d) ₹168
  26. 26.₹135 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹30 (b) ₹120 (c) ₹15 (d) ₹105
  27. 27.₹385 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹175 (b) ₹35 (c) ₹210 (d) ₹245
  28. 28.If 7 kites cost ₹161, how much do 4 kites cost? (a) ₹115 (b) ₹92 (c) ₹644 (d) ₹158
  29. 29.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 17 days (d) 16 days
  30. 30.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 15 days (c) 5 days (d) 35 days
  31. 31.If 4 kites cost ₹52, how much do 10 kites cost? (a) ₹58 (b) ₹520 (c) ₹130 (d) ₹143
  32. 32.If 8 notebooks cost ₹136, how much do 6 notebooks cost? (a) ₹102 (b) ₹816 (c) ₹119 (d) ₹134
  33. 33.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 45 days (d) 9 days
  34. 34.If 8 notebooks cost ₹64, how much do 5 notebooks cost? (a) ₹48 (b) ₹61 (c) ₹40 (d) ₹320
  35. 35.₹440 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹40 (b) ₹320 (c) ₹120 (d) ₹220
  36. 36.₹161 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹69 (b) ₹92 (c) ₹115 (d) ₹23
  37. 37.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 15 days (d) 16 days
  38. 38.If 3 kites cost ₹51, how much do 7 kites cost? (a) ₹136 (b) ₹119 (c) ₹357 (d) ₹55
  39. 39.₹48 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹8 (b) ₹48 (c) ₹40 (d) ₹24
  40. 40.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 9 days

Answer key

  1. 16 days
  2. ₹100
  3. ₹32
  4. ₹405
  5. ₹322
  6. ₹81
  7. ₹8
  8. ₹156
  9. ₹10
  10. ₹42
  11. ₹77
  12. 8 days
  13. ₹100
  14. ₹112
  15. 2 days
  16. ₹243
  17. 21 days
  18. ₹60
  19. ₹210
  20. 15 days
  21. ₹6
  22. ₹132
  23. ₹161
  24. ₹308
  25. ₹21
  26. ₹105
  27. ₹210
  28. ₹92
  29. 16 days
  30. 35 days
  31. ₹130
  32. ₹102
  33. 45 days
  34. ₹40
  35. ₹320
  36. ₹92
  37. 16 days
  38. ₹119
  39. ₹40
  40. 7 days

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