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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 125 · 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.₹120 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹60 (b) ₹80 (c) ₹40 (d) ₹120
  2. 2.8 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 12 days (c) 13 days (d) 17 days
  3. 3.₹120 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹60 (b) ₹90 (c) ₹120 (d) ₹30
  4. 4.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 18 days (c) 4 days (d) 5 days
  5. 5.₹350 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹50 (b) ₹175 (c) ₹300 (d) ₹350
  6. 6.If 7 notebooks cost ₹77, how much do 5 notebooks cost? (a) ₹55 (b) ₹66 (c) ₹75 (d) ₹385
  7. 7.If 9 pens cost ₹36, how much do 10 pens cost? (a) ₹360 (b) ₹44 (c) ₹40 (d) ₹37
  8. 8.₹209 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹38 (b) ₹171 (c) ₹19 (d) ₹190
  9. 9.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 21 days (d) 22 days
  10. 10.If 6 mangoes cost ₹120, how much do 4 mangoes cost? (a) ₹480 (b) ₹80 (c) ₹100 (d) ₹118
  11. 11.8 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 8 days (d) 7 days
  12. 12.If 4 pens cost ₹36, how much do 3 pens cost? (a) ₹36 (b) ₹108 (c) ₹35 (d) ₹27
  13. 13.6 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 14 days (d) 8 days
  14. 14.If 4 pens cost ₹32, how much do 12 pens cost? (a) ₹384 (b) ₹40 (c) ₹104 (d) ₹96
  15. 15.If 4 kites cost ₹72, how much do 3 kites cost? (a) ₹54 (b) ₹71 (c) ₹216 (d) ₹72
  16. 16.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 36 days (c) 19 days (d) 35 days
  17. 17.If 6 pens cost ₹24, how much do 8 pens cost? (a) ₹32 (b) ₹36 (c) ₹192 (d) ₹26
  18. 18.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 17 days (d) 16 days
  19. 19.If 4 kites cost ₹88, how much do 5 kites cost? (a) ₹132 (b) ₹89 (c) ₹440 (d) ₹110
  20. 20.₹60 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹30 (b) ₹25 (c) ₹35 (d) ₹5
  21. 21.If 4 pens cost ₹92, how much do 3 pens cost? (a) ₹276 (b) ₹92 (c) ₹69 (d) ₹91
  22. 22.If 7 mangoes cost ₹21, how much do 9 mangoes cost? (a) ₹23 (b) ₹189 (c) ₹30 (d) ₹27
  23. 23.If 4 notebooks cost ₹28, how much do 7 notebooks cost? (a) ₹196 (b) ₹31 (c) ₹56 (d) ₹49
  24. 24.If 7 mangoes cost ₹112, how much do 11 mangoes cost? (a) ₹1232 (b) ₹176 (c) ₹192 (d) ₹116
  25. 25.If 9 kites cost ₹189, how much do 10 kites cost? (a) ₹1890 (b) ₹231 (c) ₹210 (d) ₹190
  26. 26.If 2 mangoes cost ₹16, how much do 9 mangoes cost? (a) ₹23 (b) ₹72 (c) ₹80 (d) ₹144
  27. 27.₹210 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹168 (b) ₹210 (c) ₹42 (d) ₹105
  28. 28.If 6 mangoes cost ₹30, how much do 8 mangoes cost? (a) ₹32 (b) ₹45 (c) ₹40 (d) ₹240
  29. 29.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 14 days (b) 18 days (c) 3 days (d) 2 days
  30. 30.8 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 9 days (c) 7 days (d) 8 days
  31. 31.5 workers can build a wall in 12 days. How many days will 10 workers take, working at the same speed? (a) 24 days (b) 7 days (c) 6 days (d) 17 days
  32. 32.If 3 mangoes cost ₹45, how much do 5 mangoes cost? (a) ₹75 (b) ₹90 (c) ₹47 (d) ₹225
  33. 33.If 8 pens cost ₹104, how much do 10 pens cost? (a) ₹143 (b) ₹130 (c) ₹1040 (d) ₹106
  34. 34.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 25 days (c) 13 days (d) 7 days
  35. 35.₹88 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹16 (b) ₹8 (c) ₹44 (d) ₹72
  36. 36.If 2 mangoes cost ₹6, how much do 12 mangoes cost? (a) ₹39 (b) ₹72 (c) ₹16 (d) ₹36
  37. 37.If 9 kites cost ₹99, how much do 5 kites cost? (a) ₹66 (b) ₹495 (c) ₹55 (d) ₹95
  38. 38.If 9 pens cost ₹117, how much do 2 pens cost? (a) ₹26 (b) ₹234 (c) ₹39 (d) ₹110
  39. 39.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 11 days (c) 3 days (d) 21 days
  40. 40.₹451 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹287 (b) ₹246 (c) ₹205 (d) ₹41

Answer key

  1. ₹80
  2. 12 days
  3. ₹90
  4. 4 days
  5. ₹300
  6. ₹55
  7. ₹40
  8. ₹171
  9. 21 days
  10. ₹80
  11. 8 days
  12. ₹27
  13. 18 days
  14. ₹96
  15. ₹54
  16. 35 days
  17. ₹32
  18. 16 days
  19. ₹110
  20. ₹35
  21. ₹69
  22. ₹27
  23. ₹49
  24. ₹176
  25. ₹210
  26. ₹72
  27. ₹168
  28. ₹40
  29. 2 days
  30. 8 days
  31. 6 days
  32. ₹75
  33. ₹130
  34. 25 days
  35. ₹72
  36. ₹36
  37. ₹55
  38. ₹26
  39. 21 days
  40. ₹246

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