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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 559 · 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. 1.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 10 days (d) 11 days
  2. 2.₹195 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹120 (b) ₹135 (c) ₹15 (d) ₹75
  3. 3.If 7 pens cost ₹84, how much do 2 pens cost? (a) ₹79 (b) ₹36 (c) ₹24 (d) ₹168
  4. 4.₹140 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹14 (b) ₹140 (c) ₹70 (d) ₹126
  5. 5.₹80 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹80 (b) ₹10 (c) ₹70 (d) ₹40
  6. 6.₹140 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹140 (b) ₹20 (c) ₹70 (d) ₹120
  7. 7.If 2 mangoes cost ₹46, how much do 5 mangoes cost? (a) ₹115 (b) ₹230 (c) ₹49 (d) ₹138
  8. 8.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 4 days (c) 7 days (d) 25 days
  9. 9.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 7 days
  10. 10.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 16 days (c) 15 days (d) 11 days
  11. 11.If 7 kites cost ₹70, how much do 8 kites cost? (a) ₹90 (b) ₹560 (c) ₹71 (d) ₹80
  12. 12.If 3 mangoes cost ₹57, how much do 2 mangoes cost? (a) ₹38 (b) ₹56 (c) ₹57 (d) ₹114
  13. 13.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 17 days (c) 44 days (d) 5 days
  14. 14.₹63 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹9 (b) ₹27 (c) ₹45 (d) ₹36
  15. 15.If 6 pens cost ₹126, how much do 7 pens cost? (a) ₹127 (b) ₹882 (c) ₹168 (d) ₹147
  16. 16.If 9 pens cost ₹135, how much do 6 pens cost? (a) ₹810 (b) ₹90 (c) ₹105 (d) ₹132
  17. 17.4 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) 27 days (d) 15 days
  18. 18.If 4 kites cost ₹24, how much do 2 kites cost? (a) ₹12 (b) ₹48 (c) ₹22 (d) ₹18
  19. 19.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 4 days (d) 12 days
  20. 20.If 3 notebooks cost ₹57, how much do 8 notebooks cost? (a) ₹62 (b) ₹171 (c) ₹456 (d) ₹152
  21. 21.₹60 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹10 (b) ₹30 (c) ₹50 (d) ₹60
  22. 22.If 5 kites cost ₹105, how much do 3 kites cost? (a) ₹315 (b) ₹103 (c) ₹84 (d) ₹63
  23. 23.₹81 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹81 (b) ₹73 (c) ₹9 (d) ₹72
  24. 24.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 33 days (c) 32 days (d) 14 days
  25. 25.₹77 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹63 (b) ₹56 (c) ₹21 (d) ₹7
  26. 26.If 9 kites cost ₹63, how much do 7 kites cost? (a) ₹61 (b) ₹49 (c) ₹56 (d) ₹441
  27. 27.₹84 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹14 (b) ₹42 (c) ₹84 (d) ₹70
  28. 28.₹220 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹44 (b) ₹110 (c) ₹132 (d) ₹88
  29. 29.If 8 notebooks cost ₹80, how much do 9 notebooks cost? (a) ₹720 (b) ₹100 (c) ₹90 (d) ₹81
  30. 30.If 4 pens cost ₹24, how much do 2 pens cost? (a) ₹18 (b) ₹48 (c) ₹12 (d) ₹22
  31. 31.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 6 days (d) 2 days
  32. 32.₹385 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹35 (b) ₹245 (c) ₹140 (d) ₹280
  33. 33.₹235 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹141 (b) ₹47 (c) ₹94 (d) ₹188
  34. 34.If 8 pens cost ₹168, how much do 9 pens cost? (a) ₹1512 (b) ₹189 (c) ₹169 (d) ₹210
  35. 35.If 8 kites cost ₹88, how much do 3 kites cost? (a) ₹83 (b) ₹264 (c) ₹44 (d) ₹33
  36. 36.5 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) 4 days (d) 6 days
  37. 37.₹60 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹6 (b) ₹30 (c) ₹42 (d) ₹18
  38. 38.If 2 mangoes cost ₹44, how much do 3 mangoes cost? (a) ₹88 (b) ₹45 (c) ₹66 (d) ₹132
  39. 39.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 4 days (d) 11 days
  40. 40.If 6 pens cost ₹42, how much do 4 pens cost? (a) ₹168 (b) ₹40 (c) ₹28 (d) ₹35

Answer key

  1. 10 days
  2. ₹120
  3. ₹24
  4. ₹126
  5. ₹70
  6. ₹120
  7. ₹115
  8. 25 days
  9. 3 days
  10. 15 days
  11. ₹80
  12. ₹38
  13. 44 days
  14. ₹36
  15. ₹147
  16. ₹90
  17. 26 days
  18. ₹12
  19. 12 days
  20. ₹152
  21. ₹50
  22. ₹63
  23. ₹72
  24. 32 days
  25. ₹56
  26. ₹49
  27. ₹70
  28. ₹132
  29. ₹90
  30. ₹12
  31. 8 days
  32. ₹245
  33. ₹141
  34. ₹189
  35. ₹33
  36. 5 days
  37. ₹42
  38. ₹66
  39. 3 days
  40. ₹28

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