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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 203 · 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.If 6 notebooks cost ₹126, how much do 10 notebooks cost? (a) ₹210 (b) ₹130 (c) ₹1260 (d) ₹231
  2. 2.If 8 mangoes cost ₹48, how much do 6 mangoes cost? (a) ₹42 (b) ₹46 (c) ₹288 (d) ₹36
  3. 3.If 6 kites cost ₹60, how much do 4 kites cost? (a) ₹40 (b) ₹58 (c) ₹50 (d) ₹240
  4. 4.If 5 mangoes cost ₹50, how much do 11 mangoes cost? (a) ₹120 (b) ₹56 (c) ₹550 (d) ₹110
  5. 5.If 5 pens cost ₹35, how much do 6 pens cost? (a) ₹42 (b) ₹210 (c) ₹49 (d) ₹36
  6. 6.₹51 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹35 (b) ₹17 (c) ₹34 (d) ₹51
  7. 7.₹72 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹9 (b) ₹45 (c) ₹36 (d) ₹27
  8. 8.9 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 11 days (d) 12 days
  9. 9.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 29 days (c) 13 days (d) 28 days
  10. 10.₹84 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹42 (b) ₹12 (c) ₹60 (d) ₹24
  11. 11.₹187 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹136 (b) ₹51 (c) ₹153 (d) ₹17
  12. 12.If 9 notebooks cost ₹225, how much do 12 notebooks cost? (a) ₹325 (b) ₹2700 (c) ₹228 (d) ₹300
  13. 13.₹72 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹36 (b) ₹72 (c) ₹48 (d) ₹24
  14. 14.₹168 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹63 (b) ₹84 (c) ₹21 (d) ₹105
  15. 15.If 2 pens cost ₹16, how much do 9 pens cost? (a) ₹144 (b) ₹72 (c) ₹80 (d) ₹23
  16. 16.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹56 (b) ₹35 (c) ₹7 (d) ₹63
  17. 17.If 4 notebooks cost ₹88, how much do 11 notebooks cost? (a) ₹264 (b) ₹95 (c) ₹242 (d) ₹968
  18. 18.If 7 pens cost ₹126, how much do 4 pens cost? (a) ₹123 (b) ₹72 (c) ₹90 (d) ₹504
  19. 19.If 2 notebooks cost ₹20, how much do 11 notebooks cost? (a) ₹29 (b) ₹110 (c) ₹120 (d) ₹220
  20. 20.If 8 pens cost ₹32, how much do 12 pens cost? (a) ₹52 (b) ₹384 (c) ₹48 (d) ₹36
  21. 21.₹63 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹7 (b) ₹42 (c) ₹28 (d) ₹35
  22. 22.If 3 pens cost ₹72, how much do 4 pens cost? (a) ₹73 (b) ₹288 (c) ₹120 (d) ₹96
  23. 23.9 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 9 days (d) 8 days
  24. 24.₹189 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹105 (b) ₹21 (c) ₹126 (d) ₹84
  25. 25.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 24 days (d) 25 days
  26. 26.₹288 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹120 (b) ₹168 (c) ₹144 (d) ₹24
  27. 27.₹270 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹135 (b) ₹120 (c) ₹150 (d) ₹30
  28. 28.If 4 kites cost ₹24, how much do 10 kites cost? (a) ₹66 (b) ₹60 (c) ₹30 (d) ₹240
  29. 29.₹40 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹20 (b) ₹30 (c) ₹10 (d) ₹40
  30. 30.If 2 notebooks cost ₹12, how much do 7 notebooks cost? (a) ₹17 (b) ₹84 (c) ₹42 (d) ₹48
  31. 31.6 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 2 days (d) 14 days
  32. 32.If 7 notebooks cost ₹28, how much do 3 notebooks cost? (a) ₹16 (b) ₹84 (c) ₹24 (d) ₹12
  33. 33.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 41 days (b) 16 days (c) 40 days (d) 4 days
  34. 34.If 9 kites cost ₹189, how much do 8 kites cost? (a) ₹1512 (b) ₹168 (c) ₹188 (d) ₹189
  35. 35.If 6 mangoes cost ₹48, how much do 5 mangoes cost? (a) ₹240 (b) ₹48 (c) ₹47 (d) ₹40
  36. 36.₹225 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹100 (b) ₹125 (c) ₹25 (d) ₹150
  37. 37.If 2 kites cost ₹18, how much do 6 kites cost? (a) ₹63 (b) ₹54 (c) ₹108 (d) ₹22
  38. 38.₹48 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹16 (b) ₹32 (c) ₹24 (d) ₹48
  39. 39.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 18 days (c) 48 days (d) 3 days
  40. 40.₹175 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹70 (b) ₹105 (c) ₹35 (d) ₹140

Answer key

  1. ₹210
  2. ₹36
  3. ₹40
  4. ₹110
  5. ₹42
  6. ₹34
  7. ₹45
  8. 12 days
  9. 28 days
  10. ₹60
  11. ₹136
  12. ₹300
  13. ₹48
  14. ₹105
  15. ₹72
  16. ₹56
  17. ₹242
  18. ₹72
  19. ₹110
  20. ₹48
  21. ₹35
  22. ₹96
  23. 9 days
  24. ₹105
  25. 24 days
  26. ₹168
  27. ₹150
  28. ₹60
  29. ₹30
  30. ₹42
  31. 4 days
  32. ₹12
  33. 40 days
  34. ₹168
  35. ₹40
  36. ₹125
  37. ₹54
  38. ₹32
  39. 48 days
  40. ₹105

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