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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 118 · 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 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 4 days (d) 3 days
  2. 2.If 2 mangoes cost ₹38, how much do 3 mangoes cost? (a) ₹76 (b) ₹39 (c) ₹57 (d) ₹114
  3. 3.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 11 days (d) 15 days
  4. 4.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 8 days (c) 9 days (d) 10 days
  5. 5.₹306 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹306 (b) ₹34 (c) ₹272 (d) ₹153
  6. 6.If 4 pens cost ₹72, how much do 5 pens cost? (a) ₹360 (b) ₹90 (c) ₹73 (d) ₹108
  7. 7.₹352 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹176 (b) ₹224 (c) ₹32 (d) ₹128
  8. 8.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 16 days (d) 10 days
  9. 9.₹154 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹42 (b) ₹77 (c) ₹14 (d) ₹112
  10. 10.If 9 notebooks cost ₹45, how much do 11 notebooks cost? (a) ₹47 (b) ₹495 (c) ₹55 (d) ₹60
  11. 11.If 3 notebooks cost ₹63, how much do 4 notebooks cost? (a) ₹64 (b) ₹105 (c) ₹252 (d) ₹84
  12. 12.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 5 days (d) 6 days
  13. 13.If 8 pens cost ₹128, how much do 11 pens cost? (a) ₹192 (b) ₹1408 (c) ₹131 (d) ₹176
  14. 14.₹120 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹50 (b) ₹10 (c) ₹60 (d) ₹70
  15. 15.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 29 days (c) 3 days (d) 13 days
  16. 16.If 4 notebooks cost ₹16, how much do 3 notebooks cost? (a) ₹12 (b) ₹15 (c) ₹48 (d) ₹16
  17. 17.₹315 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹315 (b) ₹35 (c) ₹281 (d) ₹280
  18. 18.₹385 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹210 (b) ₹175 (c) ₹245 (d) ₹35
  19. 19.If 8 pens cost ₹144, how much do 5 pens cost? (a) ₹108 (b) ₹141 (c) ₹720 (d) ₹90
  20. 20.₹102 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹51 (b) ₹85 (c) ₹17 (d) ₹102
  21. 21.₹70 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹7 (b) ₹21 (c) ₹35 (d) ₹49
  22. 22.8 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 24 days (c) 8 days (d) 6 days
  23. 23.If 5 kites cost ₹25, how much do 8 kites cost? (a) ₹45 (b) ₹28 (c) ₹200 (d) ₹40
  24. 24.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 13 days (d) 25 days
  25. 25.If 7 mangoes cost ₹168, how much do 2 mangoes cost? (a) ₹336 (b) ₹72 (c) ₹163 (d) ₹48
  26. 26.If 9 kites cost ₹225, how much do 11 kites cost? (a) ₹275 (b) ₹2475 (c) ₹227 (d) ₹300
  27. 27.₹528 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹44 (b) ₹220 (c) ₹308 (d) ₹264
  28. 28.₹153 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹136 (b) ₹119 (c) ₹34 (d) ₹17
  29. 29.If 3 kites cost ₹27, how much do 5 kites cost? (a) ₹29 (b) ₹54 (c) ₹135 (d) ₹45
  30. 30.If 5 mangoes cost ₹50, how much do 8 mangoes cost? (a) ₹90 (b) ₹80 (c) ₹400 (d) ₹53
  31. 31.If 5 notebooks cost ₹50, how much do 3 notebooks cost? (a) ₹40 (b) ₹30 (c) ₹150 (d) ₹48
  32. 32.If 6 notebooks cost ₹138, how much do 11 notebooks cost? (a) ₹276 (b) ₹253 (c) ₹143 (d) ₹1518
  33. 33.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 11 days (d) 20 days
  34. 34.₹217 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹186 (b) ₹155 (c) ₹31 (d) ₹62
  35. 35.If 8 pens cost ₹48, how much do 2 pens cost? (a) ₹18 (b) ₹12 (c) ₹42 (d) ₹96
  36. 36.If 3 notebooks cost ₹15, how much do 4 notebooks cost? (a) ₹16 (b) ₹20 (c) ₹25 (d) ₹60
  37. 37.₹286 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹26 (b) ₹104 (c) ₹143 (d) ₹182
  38. 38.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 9 days (d) 2 days
  39. 39.If 4 notebooks cost ₹28, how much do 10 notebooks cost? (a) ₹280 (b) ₹34 (c) ₹77 (d) ₹70
  40. 40.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 5 days (d) 6 days

Answer key

  1. 9 days
  2. ₹57
  3. 15 days
  4. 9 days
  5. ₹272
  6. ₹90
  7. ₹224
  8. 10 days
  9. ₹112
  10. ₹55
  11. ₹84
  12. 7 days
  13. ₹176
  14. ₹70
  15. 28 days
  16. ₹12
  17. ₹280
  18. ₹210
  19. ₹90
  20. ₹85
  21. ₹49
  22. 24 days
  23. ₹40
  24. 9 days
  25. ₹48
  26. ₹275
  27. ₹308
  28. ₹119
  29. ₹45
  30. ₹80
  31. ₹30
  32. ₹253
  33. 20 days
  34. ₹155
  35. ₹12
  36. ₹20
  37. ₹182
  38. 2 days
  39. ₹70
  40. 6 days

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