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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 881 · 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 12 days. How many days will 6 workers take, working at the same speed? (a) 14 days (b) 8 days (c) 10 days (d) 18 days
  2. 2.₹450 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹200 (b) ₹225 (c) ₹250 (d) ₹50
  3. 3.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 6 days (c) 7 days (d) 5 days
  4. 4.If 5 notebooks cost ₹15, how much do 6 notebooks cost? (a) ₹18 (b) ₹16 (c) ₹21 (d) ₹90
  5. 5.₹141 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹94 (b) ₹95 (c) ₹141 (d) ₹47
  6. 6.₹70 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹45 (b) ₹25 (c) ₹5 (d) ₹35
  7. 7.₹99 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹18 (b) ₹90 (c) ₹9 (d) ₹81
  8. 8.If 8 notebooks cost ₹136, how much do 10 notebooks cost? (a) ₹1360 (b) ₹187 (c) ₹170 (d) ₹138
  9. 9.If 3 notebooks cost ₹51, how much do 7 notebooks cost? (a) ₹136 (b) ₹119 (c) ₹55 (d) ₹357
  10. 10.If 4 mangoes cost ₹52, how much do 5 mangoes cost? (a) ₹78 (b) ₹53 (c) ₹260 (d) ₹65
  11. 11.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 16 days (c) 10 days (d) 4 days
  12. 12.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 6 days (d) 12 days
  13. 13.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 37 days (c) 3 days (d) 15 days
  14. 14.If 8 pens cost ₹176, how much do 2 pens cost? (a) ₹170 (b) ₹352 (c) ₹66 (d) ₹44
  15. 15.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 3 days (d) 2 days
  16. 16.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 8 days (d) 10 days
  17. 17.If 7 notebooks cost ₹154, how much do 2 notebooks cost? (a) ₹66 (b) ₹149 (c) ₹308 (d) ₹44
  18. 18.If 2 notebooks cost ₹46, how much do 11 notebooks cost? (a) ₹55 (b) ₹506 (c) ₹276 (d) ₹253
  19. 19.If 7 notebooks cost ₹56, how much do 8 notebooks cost? (a) ₹448 (b) ₹64 (c) ₹72 (d) ₹57
  20. 20.If 3 pens cost ₹21, how much do 5 pens cost? (a) ₹42 (b) ₹23 (c) ₹35 (d) ₹105
  21. 21.₹352 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹132 (b) ₹176 (c) ₹220 (d) ₹44
  22. 22.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 16 days (c) 11 days (d) 15 days
  23. 23.₹140 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹70 (b) ₹60 (c) ₹20 (d) ₹80
  24. 24.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 48 days (c) 6 days (d) 18 days
  25. 25.₹171 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹114 (b) ₹76 (c) ₹19 (d) ₹95
  26. 26.₹187 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹17 (b) ₹136 (c) ₹153 (d) ₹51
  27. 27.If 3 kites cost ₹39, how much do 2 kites cost? (a) ₹38 (b) ₹26 (c) ₹78 (d) ₹39
  28. 28.₹168 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹42 (b) ₹126 (c) ₹168 (d) ₹84
  29. 29.If 8 notebooks cost ₹80, how much do 10 notebooks cost? (a) ₹82 (b) ₹110 (c) ₹800 (d) ₹100
  30. 30.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 4 days (d) 19 days
  31. 31.If 9 mangoes cost ₹225, how much do 2 mangoes cost? (a) ₹75 (b) ₹450 (c) ₹50 (d) ₹218
  32. 32.₹312 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹192 (b) ₹24 (c) ₹156 (d) ₹120
  33. 33.₹57 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹39 (b) ₹19 (c) ₹57 (d) ₹38
  34. 34.If 9 mangoes cost ₹153, how much do 11 mangoes cost? (a) ₹187 (b) ₹1683 (c) ₹155 (d) ₹204
  35. 35.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 14 days (b) 13 days (c) 16 days (d) 12 days
  36. 36.If 3 mangoes cost ₹45, how much do 10 mangoes cost? (a) ₹52 (b) ₹165 (c) ₹150 (d) ₹450
  37. 37.₹63 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹7 (b) ₹14 (c) ₹56 (d) ₹49
  38. 38.If 7 mangoes cost ₹112, how much do 4 mangoes cost? (a) ₹64 (b) ₹109 (c) ₹448 (d) ₹80
  39. 39.₹87 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹29 (b) ₹59 (c) ₹58 (d) ₹87
  40. 40.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 4 days (d) 5 days

Answer key

  1. 8 days
  2. ₹250
  3. 6 days
  4. ₹18
  5. ₹94
  6. ₹45
  7. ₹81
  8. ₹170
  9. ₹119
  10. ₹65
  11. 16 days
  12. 18 days
  13. 36 days
  14. ₹44
  15. 2 days
  16. 9 days
  17. ₹44
  18. ₹253
  19. ₹64
  20. ₹35
  21. ₹220
  22. 15 days
  23. ₹80
  24. 48 days
  25. ₹95
  26. ₹136
  27. ₹26
  28. ₹126
  29. ₹100
  30. 3 days
  31. ₹50
  32. ₹192
  33. ₹38
  34. ₹187
  35. 12 days
  36. ₹150
  37. ₹49
  38. ₹64
  39. ₹58
  40. 4 days

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