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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 111 · 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.₹407 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹222 (b) ₹37 (c) ₹185 (d) ₹259
  2. 2.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 11 days (d) 2 days
  3. 3.₹126 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹45 (b) ₹63 (c) ₹9 (d) ₹81
  4. 4.If 3 kites cost ₹33, how much do 9 kites cost? (a) ₹297 (b) ₹99 (c) ₹39 (d) ₹110
  5. 5.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 13 days (c) 25 days (d) 4 days
  6. 6.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 8 days (d) 6 days
  7. 7.If 3 notebooks cost ₹36, how much do 10 notebooks cost? (a) ₹43 (b) ₹360 (c) ₹120 (d) ₹132
  8. 8.₹144 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹54 (b) ₹18 (c) ₹90 (d) ₹72
  9. 9.If 4 kites cost ₹60, how much do 5 kites cost? (a) ₹75 (b) ₹90 (c) ₹300 (d) ₹61
  10. 10.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 2 days (d) 7 days
  11. 11.₹48 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹24 (b) ₹16 (c) ₹48 (d) ₹32
  12. 12.If 7 notebooks cost ₹168, how much do 2 notebooks cost? (a) ₹48 (b) ₹336 (c) ₹72 (d) ₹163
  13. 13.If 4 mangoes cost ₹100, how much do 5 mangoes cost? (a) ₹101 (b) ₹500 (c) ₹150 (d) ₹125
  14. 14.If 2 kites cost ₹20, how much do 7 kites cost? (a) ₹25 (b) ₹140 (c) ₹70 (d) ₹80
  15. 15.If 9 pens cost ₹126, how much do 2 pens cost? (a) ₹28 (b) ₹119 (c) ₹42 (d) ₹252
  16. 16.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 14 days (d) 15 days
  17. 17.If 7 mangoes cost ₹35, how much do 9 mangoes cost? (a) ₹315 (b) ₹45 (c) ₹37 (d) ₹50
  18. 18.If 8 notebooks cost ₹152, how much do 3 notebooks cost? (a) ₹147 (b) ₹57 (c) ₹456 (d) ₹76
  19. 19.If 6 mangoes cost ₹18, how much do 5 mangoes cost? (a) ₹18 (b) ₹17 (c) ₹90 (d) ₹15
  20. 20.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 12 days (d) 11 days
  21. 21.If 3 mangoes cost ₹51, how much do 9 mangoes cost? (a) ₹57 (b) ₹459 (c) ₹153 (d) ₹170
  22. 22.If 6 mangoes cost ₹60, how much do 4 mangoes cost? (a) ₹58 (b) ₹40 (c) ₹240 (d) ₹50
  23. 23.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 28 days (c) 29 days (d) 1 day
  24. 24.If 4 mangoes cost ₹40, how much do 2 mangoes cost? (a) ₹80 (b) ₹20 (c) ₹38 (d) ₹30
  25. 25.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 9 days (c) 16 days (d) 15 days
  26. 26.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 19 days (c) 4 days (d) 3 days
  27. 27.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 11 days (c) 19 days (d) 17 days
  28. 28.If 7 pens cost ₹140, how much do 11 pens cost? (a) ₹240 (b) ₹1540 (c) ₹220 (d) ₹144
  29. 29.₹45 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹9 (b) ₹18 (c) ₹36 (d) ₹27
  30. 30.If 9 notebooks cost ₹54, how much do 2 notebooks cost? (a) ₹47 (b) ₹18 (c) ₹12 (d) ₹108
  31. 31.₹110 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹10 (b) ₹40 (c) ₹70 (d) ₹55
  32. 32.₹175 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹175 (b) ₹151 (c) ₹25 (d) ₹150
  33. 33.₹91 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹39 (b) ₹65 (c) ₹52 (d) ₹13
  34. 34.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 37 days (b) 36 days (c) 15 days (d) 1 day
  35. 35.₹266 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹152 (b) ₹38 (c) ₹133 (d) ₹114
  36. 36.₹126 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹14 (b) ₹70 (c) ₹56 (d) ₹63
  37. 37.₹135 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹45 (b) ₹135 (c) ₹91 (d) ₹90
  38. 38.If 7 mangoes cost ₹21, how much do 3 mangoes cost? (a) ₹17 (b) ₹12 (c) ₹63 (d) ₹9
  39. 39.If 6 mangoes cost ₹18, how much do 4 mangoes cost? (a) ₹72 (b) ₹15 (c) ₹12 (d) ₹16
  40. 40.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 15 days (b) 6 days (c) 20 days (d) 5 days

Answer key

  1. ₹222
  2. 3 days
  3. ₹81
  4. ₹99
  5. 25 days
  6. 7 days
  7. ₹120
  8. ₹90
  9. ₹75
  10. 2 days
  11. ₹32
  12. ₹48
  13. ₹125
  14. ₹70
  15. ₹28
  16. 14 days
  17. ₹45
  18. ₹57
  19. ₹15
  20. 3 days
  21. ₹153
  22. ₹40
  23. 28 days
  24. ₹20
  25. 15 days
  26. 3 days
  27. 18 days
  28. ₹220
  29. ₹27
  30. ₹12
  31. ₹70
  32. ₹150
  33. ₹52
  34. 36 days
  35. ₹152
  36. ₹70
  37. ₹90
  38. ₹9
  39. ₹12
  40. 5 days

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