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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 740 · 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. 1.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 19 days
  2. 2.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 18 days (b) 5 days (c) 4 days (d) 3 days
  3. 3.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 10 days (d) 1 day
  4. 4.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 20 days (d) 6 days
  5. 5.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 5 days (d) 45 days
  6. 6.₹220 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹100 (b) ₹120 (c) ₹20 (d) ₹110
  7. 7.If 5 notebooks cost ₹35, how much do 4 notebooks cost? (a) ₹140 (b) ₹34 (c) ₹28 (d) ₹35
  8. 8.₹27 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹19 (b) ₹27 (c) ₹9 (d) ₹18
  9. 9.₹165 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹75 (b) ₹90 (c) ₹15 (d) ₹105
  10. 10.If 4 kites cost ₹80, how much do 7 kites cost? (a) ₹140 (b) ₹83 (c) ₹560 (d) ₹160
  11. 11.If 9 notebooks cost ₹63, how much do 10 notebooks cost? (a) ₹70 (b) ₹630 (c) ₹64 (d) ₹77
  12. 12.₹336 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹126 (b) ₹42 (c) ₹168 (d) ₹210
  13. 13.If 7 mangoes cost ₹35, how much do 8 mangoes cost? (a) ₹40 (b) ₹280 (c) ₹36 (d) ₹45
  14. 14.9 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) 10 days (d) 8 days
  15. 15.If 5 kites cost ₹25, how much do 9 kites cost? (a) ₹225 (b) ₹50 (c) ₹29 (d) ₹45
  16. 16.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 2 days (c) 3 days (d) 1 day
  17. 17.₹52 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹13 (b) ₹26 (c) ₹39 (d) ₹52
  18. 18.If 7 mangoes cost ₹175, how much do 8 mangoes cost? (a) ₹1400 (b) ₹176 (c) ₹200 (d) ₹225
  19. 19.If 5 notebooks cost ₹45, how much do 3 notebooks cost? (a) ₹27 (b) ₹43 (c) ₹36 (d) ₹135
  20. 20.₹273 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹117 (b) ₹156 (c) ₹39 (d) ₹195
  21. 21.₹95 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹38 (b) ₹19 (c) ₹57 (d) ₹76
  22. 22.₹384 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹32 (b) ₹160 (c) ₹224 (d) ₹192
  23. 23.₹66 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹12 (b) ₹6 (c) ₹33 (d) ₹54
  24. 24.If 4 notebooks cost ₹40, how much do 6 notebooks cost? (a) ₹70 (b) ₹42 (c) ₹60 (d) ₹240
  25. 25.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 14 days (d) 7 days
  26. 26.₹132 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹12 (b) ₹24 (c) ₹108 (d) ₹66
  27. 27.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 15 days (d) 14 days
  28. 28.₹117 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹78 (b) ₹39 (c) ₹117 (d) ₹79
  29. 29.₹25 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹21 (b) ₹20 (c) ₹5 (d) ₹25
  30. 30.3 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 21 days (b) 4 days (c) 3 days (d) 48 days
  31. 31.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 14 days (d) 11 days
  32. 32.If 4 kites cost ₹12, how much do 3 kites cost? (a) ₹9 (b) ₹11 (c) ₹12 (d) ₹36
  33. 33.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 14 days (b) 3 days (c) 2 days (d) 18 days
  34. 34.₹231 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹147 (b) ₹126 (c) ₹105 (d) ₹21
  35. 35.If 6 mangoes cost ₹36, how much do 7 mangoes cost? (a) ₹37 (b) ₹48 (c) ₹252 (d) ₹42
  36. 36.₹135 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹108 (b) ₹54 (c) ₹27 (d) ₹81
  37. 37.If 7 kites cost ₹70, how much do 6 kites cost? (a) ₹420 (b) ₹70 (c) ₹60 (d) ₹69
  38. 38.If 4 kites cost ₹44, how much do 11 kites cost? (a) ₹484 (b) ₹132 (c) ₹121 (d) ₹51
  39. 39.If 2 kites cost ₹36, how much do 4 kites cost? (a) ₹90 (b) ₹144 (c) ₹72 (d) ₹38
  40. 40.If 2 kites cost ₹12, how much do 11 kites cost? (a) ₹132 (b) ₹21 (c) ₹72 (d) ₹66

Answer key

  1. 3 days
  2. 4 days
  3. 9 days
  4. 5 days
  5. 45 days
  6. ₹120
  7. ₹28
  8. ₹18
  9. ₹90
  10. ₹140
  11. ₹70
  12. ₹210
  13. ₹40
  14. 9 days
  15. ₹45
  16. 2 days
  17. ₹39
  18. ₹200
  19. ₹27
  20. ₹156
  21. ₹57
  22. ₹224
  23. ₹54
  24. ₹60
  25. 8 days
  26. ₹108
  27. 14 days
  28. ₹78
  29. ₹20
  30. 3 days
  31. 14 days
  32. ₹9
  33. 2 days
  34. ₹126
  35. ₹42
  36. ₹81
  37. ₹60
  38. ₹121
  39. ₹72
  40. ₹66

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