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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 690 · 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. 1.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 10 days (c) 11 days (d) 9 days
  2. 2.If 3 notebooks cost ₹24, how much do 4 notebooks cost? (a) ₹25 (b) ₹40 (c) ₹32 (d) ₹96
  3. 3.₹189 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹42 (b) ₹168 (c) ₹21 (d) ₹147
  4. 4.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 29 days (c) 28 days (d) 3 days
  5. 5.If 3 pens cost ₹24, how much do 11 pens cost? (a) ₹32 (b) ₹96 (c) ₹88 (d) ₹264
  6. 6.If 9 pens cost ₹27, how much do 6 pens cost? (a) ₹24 (b) ₹162 (c) ₹21 (d) ₹18
  7. 7.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 55 days (b) 19 days (c) 54 days (d) 5 days
  8. 8.If 2 notebooks cost ₹18, how much do 12 notebooks cost? (a) ₹216 (b) ₹108 (c) ₹117 (d) ₹28
  9. 9.₹105 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹15 (b) ₹60 (c) ₹45 (d) ₹75
  10. 10.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 48 days (c) 3 days (d) 18 days
  11. 11.If 9 pens cost ₹27, how much do 5 pens cost? (a) ₹135 (b) ₹18 (c) ₹15 (d) ₹23
  12. 12.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 9 days (d) 24 days
  13. 13.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 45 days (b) 9 days (c) 5 days (d) 21 days
  14. 14.₹275 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹175 (b) ₹100 (c) ₹25 (d) ₹200
  15. 15.If 3 kites cost ₹63, how much do 11 kites cost? (a) ₹231 (b) ₹693 (c) ₹71 (d) ₹252
  16. 16.If 5 notebooks cost ₹80, how much do 3 notebooks cost? (a) ₹78 (b) ₹48 (c) ₹240 (d) ₹64
  17. 17.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 9 days (d) 4 days
  18. 18.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 19 days (c) 9 days (d) 49 days
  19. 19.If 4 notebooks cost ₹72, how much do 5 notebooks cost? (a) ₹90 (b) ₹73 (c) ₹360 (d) ₹108
  20. 20.₹168 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹84 (b) ₹14 (c) ₹70 (d) ₹98
  21. 21.If 7 pens cost ₹84, how much do 5 pens cost? (a) ₹82 (b) ₹60 (c) ₹420 (d) ₹72
  22. 22.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 1 day (c) 22 days (d) 21 days
  23. 23.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 1 day (d) 3 days
  24. 24.If 5 kites cost ₹20, how much do 9 kites cost? (a) ₹24 (b) ₹40 (c) ₹180 (d) ₹36
  25. 25.If 7 mangoes cost ₹175, how much do 6 mangoes cost? (a) ₹175 (b) ₹1050 (c) ₹150 (d) ₹174
  26. 26.₹276 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹230 (b) ₹138 (c) ₹46 (d) ₹276
  27. 27.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 15 days (d) 27 days
  28. 28.₹77 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹66 (b) ₹11 (c) ₹67 (d) ₹77
  29. 29.₹135 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹135 (b) ₹27 (c) ₹108 (d) ₹109
  30. 30.₹297 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹27 (b) ₹81 (c) ₹243 (d) ₹216
  31. 31.₹98 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹28 (b) ₹49 (c) ₹70 (d) ₹14
  32. 32.If 7 pens cost ₹91, how much do 9 pens cost? (a) ₹130 (b) ₹93 (c) ₹117 (d) ₹819
  33. 33.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 3 days (c) 12 days (d) 4 days
  34. 34.If 9 kites cost ₹45, how much do 2 kites cost? (a) ₹90 (b) ₹15 (c) ₹10 (d) ₹38
  35. 35.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 3 days (c) 9 days (d) 12 days
  36. 36.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 10 days (c) 17 days (d) 11 days
  37. 37.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹119 (b) ₹85 (c) ₹17 (d) ₹102
  38. 38.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 34 days (b) 33 days (c) 17 days (d) 5 days
  39. 39.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 40 days (c) 39 days (d) 7 days
  40. 40.₹60 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹40 (b) ₹20 (c) ₹60 (d) ₹30

Answer key

  1. 10 days
  2. ₹32
  3. ₹147
  4. 28 days
  5. ₹88
  6. ₹18
  7. 54 days
  8. ₹108
  9. ₹60
  10. 48 days
  11. ₹15
  12. 6 days
  13. 5 days
  14. ₹175
  15. ₹231
  16. ₹48
  17. 5 days
  18. 49 days
  19. ₹90
  20. ₹98
  21. ₹60
  22. 21 days
  23. 3 days
  24. ₹36
  25. ₹150
  26. ₹230
  27. 3 days
  28. ₹66
  29. ₹108
  30. ₹216
  31. ₹70
  32. ₹117
  33. 3 days
  34. ₹10
  35. 12 days
  36. 10 days
  37. ₹119
  38. 33 days
  39. 39 days
  40. ₹40

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