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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 63 · 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. 1.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 27 days (b) 28 days (c) 19 days (d) 11 days
  2. 2.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 12 days (c) 3 days (d) 4 days
  3. 3.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 8 days (c) 9 days (d) 18 days
  4. 4.₹126 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹126 (b) ₹21 (c) ₹105 (d) ₹63
  5. 5.₹279 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹155 (b) ₹31 (c) ₹186 (d) ₹124
  6. 6.₹160 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹120 (b) ₹80 (c) ₹160 (d) ₹40
  7. 7.If 4 kites cost ₹92, how much do 2 kites cost? (a) ₹184 (b) ₹46 (c) ₹90 (d) ₹69
  8. 8.If 2 notebooks cost ₹12, how much do 8 notebooks cost? (a) ₹18 (b) ₹96 (c) ₹48 (d) ₹54
  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 2 kites cost ₹10, how much do 7 kites cost? (a) ₹35 (b) ₹70 (c) ₹15 (d) ₹40
  11. 11.If 8 kites cost ₹200, how much do 9 kites cost? (a) ₹201 (b) ₹225 (c) ₹250 (d) ₹1800
  12. 12.₹232 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹116 (b) ₹29 (c) ₹145 (d) ₹87
  13. 13.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 26 days (d) 27 days
  14. 14.₹245 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹196 (b) ₹147 (c) ₹49 (d) ₹98
  15. 15.₹228 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹95 (b) ₹19 (c) ₹114 (d) ₹133
  16. 16.If 7 pens cost ₹175, how much do 3 pens cost? (a) ₹100 (b) ₹75 (c) ₹525 (d) ₹171
  17. 17.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 5 days (d) 20 days
  18. 18.₹288 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹48 (b) ₹288 (c) ₹240 (d) ₹144
  19. 19.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 13 days
  20. 20.If 9 pens cost ₹63, how much do 4 pens cost? (a) ₹58 (b) ₹35 (c) ₹28 (d) ₹252
  21. 21.If 2 pens cost ₹8, how much do 5 pens cost? (a) ₹11 (b) ₹24 (c) ₹20 (d) ₹40
  22. 22.If 4 mangoes cost ₹84, how much do 5 mangoes cost? (a) ₹85 (b) ₹126 (c) ₹105 (d) ₹420
  23. 23.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 6 days (c) 9 days (d) 24 days
  24. 24.If 6 notebooks cost ₹144, how much do 5 notebooks cost? (a) ₹143 (b) ₹144 (c) ₹120 (d) ₹720
  25. 25.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 33 days (d) 32 days
  26. 26.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 45 days (b) 7 days (c) 23 days (d) 5 days
  27. 27.₹207 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹161 (b) ₹184 (c) ₹23 (d) ₹46
  28. 28.If 3 pens cost ₹30, how much do 4 pens cost? (a) ₹50 (b) ₹120 (c) ₹40 (d) ₹31
  29. 29.If 9 notebooks cost ₹90, how much do 8 notebooks cost? (a) ₹720 (b) ₹89 (c) ₹90 (d) ₹80
  30. 30.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 39 days (c) 17 days (d) 40 days
  31. 31.₹170 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹85 (b) ₹153 (c) ₹17 (d) ₹170
  32. 32.If 3 pens cost ₹27, how much do 5 pens cost? (a) ₹29 (b) ₹45 (c) ₹135 (d) ₹54
  33. 33.If 6 notebooks cost ₹102, how much do 10 notebooks cost? (a) ₹106 (b) ₹187 (c) ₹1020 (d) ₹170
  34. 34.₹546 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹42 (b) ₹273 (c) ₹336 (d) ₹210
  35. 35.If 3 pens cost ₹51, how much do 10 pens cost? (a) ₹170 (b) ₹187 (c) ₹58 (d) ₹510
  36. 36.If 4 notebooks cost ₹44, how much do 6 notebooks cost? (a) ₹264 (b) ₹77 (c) ₹46 (d) ₹66
  37. 37.If 3 notebooks cost ₹48, how much do 11 notebooks cost? (a) ₹192 (b) ₹56 (c) ₹176 (d) ₹528
  38. 38.If 3 notebooks cost ₹12, how much do 2 notebooks cost? (a) ₹11 (b) ₹24 (c) ₹8 (d) ₹12
  39. 39.₹252 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹108 (b) ₹126 (c) ₹36 (d) ₹144
  40. 40.If 3 mangoes cost ₹57, how much do 4 mangoes cost? (a) ₹228 (b) ₹76 (c) ₹58 (d) ₹95

Answer key

  1. 27 days
  2. 3 days
  3. 8 days
  4. ₹105
  5. ₹155
  6. ₹120
  7. ₹46
  8. ₹48
  9. 26 days
  10. ₹35
  11. ₹225
  12. ₹145
  13. 26 days
  14. ₹147
  15. ₹133
  16. ₹75
  17. 5 days
  18. ₹240
  19. 5 days
  20. ₹28
  21. ₹20
  22. ₹105
  23. 6 days
  24. ₹120
  25. 32 days
  26. 5 days
  27. ₹161
  28. ₹40
  29. ₹80
  30. 39 days
  31. ₹153
  32. ₹45
  33. ₹170
  34. ₹336
  35. ₹170
  36. ₹66
  37. ₹176
  38. ₹8
  39. ₹144
  40. ₹76

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