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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 187 · 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.If 5 mangoes cost ₹55, how much do 6 mangoes cost? (a) ₹56 (b) ₹77 (c) ₹66 (d) ₹330
  2. 2.6 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 24 days (d) 18 days
  3. 3.5 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 31 days (b) 9 days (c) 15 days (d) 30 days
  4. 4.₹189 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹21 (b) ₹42 (c) ₹168 (d) ₹147
  5. 5.8 workers can build a wall in 9 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 18 days (c) 13 days (d) 19 days
  6. 6.If 9 pens cost ₹54, how much do 8 pens cost? (a) ₹48 (b) ₹432 (c) ₹54 (d) ₹53
  7. 7.If 9 pens cost ₹99, how much do 3 pens cost? (a) ₹33 (b) ₹297 (c) ₹44 (d) ₹93
  8. 8.If 8 notebooks cost ₹80, how much do 9 notebooks cost? (a) ₹100 (b) ₹81 (c) ₹90 (d) ₹720
  9. 9.If 4 pens cost ₹60, how much do 8 pens cost? (a) ₹135 (b) ₹120 (c) ₹64 (d) ₹480
  10. 10.If 2 pens cost ₹40, how much do 3 pens cost? (a) ₹60 (b) ₹41 (c) ₹80 (d) ₹120
  11. 11.If 8 mangoes cost ₹176, how much do 12 mangoes cost? (a) ₹286 (b) ₹180 (c) ₹264 (d) ₹2112
  12. 12.If 7 pens cost ₹112, how much do 8 pens cost? (a) ₹896 (b) ₹113 (c) ₹144 (d) ₹128
  13. 13.₹180 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹162 (b) ₹18 (c) ₹90 (d) ₹180
  14. 14.If 2 pens cost ₹36, how much do 9 pens cost? (a) ₹43 (b) ₹324 (c) ₹162 (d) ₹180
  15. 15.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 9 days (c) 4 days (d) 19 days
  16. 16.₹308 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹28 (b) ₹140 (c) ₹154 (d) ₹168
  17. 17.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 8 days (d) 5 days
  18. 18.If 5 pens cost ₹45, how much do 10 pens cost? (a) ₹50 (b) ₹450 (c) ₹90 (d) ₹99
  19. 19.If 9 notebooks cost ₹198, how much do 3 notebooks cost? (a) ₹88 (b) ₹594 (c) ₹66 (d) ₹192
  20. 20.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 43 days (c) 8 days (d) 42 days
  21. 21.₹209 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹114 (b) ₹133 (c) ₹19 (d) ₹95
  22. 22.If 4 kites cost ₹96, how much do 5 kites cost? (a) ₹97 (b) ₹480 (c) ₹120 (d) ₹144
  23. 23.₹364 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹224 (b) ₹140 (c) ₹182 (d) ₹28
  24. 24.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 4 days (d) 5 days
  25. 25.If 4 notebooks cost ₹72, how much do 11 notebooks cost? (a) ₹792 (b) ₹198 (c) ₹216 (d) ₹79
  26. 26.₹552 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹46 (b) ₹276 (c) ₹322 (d) ₹230
  27. 27.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 16 days (c) 6 days (d) 24 days
  28. 28.If 2 kites cost ₹24, how much do 11 kites cost? (a) ₹33 (b) ₹264 (c) ₹144 (d) ₹132
  29. 29.₹188 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹188 (b) ₹141 (c) ₹47 (d) ₹94
  30. 30.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 12 days (c) 8 days (d) 7 days
  31. 31.If 3 mangoes cost ₹18, how much do 6 mangoes cost? (a) ₹36 (b) ₹42 (c) ₹21 (d) ₹108
  32. 32.If 5 pens cost ₹60, how much do 3 pens cost? (a) ₹58 (b) ₹36 (c) ₹180 (d) ₹48
  33. 33.If 9 pens cost ₹144, how much do 5 pens cost? (a) ₹80 (b) ₹720 (c) ₹140 (d) ₹96
  34. 34.If 9 mangoes cost ₹189, how much do 6 mangoes cost? (a) ₹126 (b) ₹147 (c) ₹1134 (d) ₹186
  35. 35.If 9 notebooks cost ₹27, how much do 12 notebooks cost? (a) ₹324 (b) ₹30 (c) ₹36 (d) ₹39
  36. 36.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 11 days
  37. 37.If 6 kites cost ₹120, how much do 2 kites cost? (a) ₹60 (b) ₹116 (c) ₹40 (d) ₹240
  38. 38.If 3 kites cost ₹69, how much do 2 kites cost? (a) ₹46 (b) ₹138 (c) ₹69 (d) ₹68
  39. 39.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 12 days (d) 11 days
  40. 40.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 6 days (c) 7 days (d) 5 days

Answer key

  1. ₹66
  2. 6 days
  3. 30 days
  4. ₹147
  5. 18 days
  6. ₹48
  7. ₹33
  8. ₹90
  9. ₹120
  10. ₹60
  11. ₹264
  12. ₹128
  13. ₹162
  14. ₹162
  15. 49 days
  16. ₹168
  17. 8 days
  18. ₹90
  19. ₹66
  20. 42 days
  21. ₹114
  22. ₹120
  23. ₹224
  24. 9 days
  25. ₹198
  26. ₹322
  27. 6 days
  28. ₹132
  29. ₹141
  30. 8 days
  31. ₹36
  32. ₹36
  33. ₹80
  34. ₹126
  35. ₹36
  36. 7 days
  37. ₹40
  38. ₹46
  39. 10 days
  40. 6 days

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