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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 477 · 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.₹228 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹114 (b) ₹133 (c) ₹19 (d) ₹95
  2. 2.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 5 days (d) 8 days
  3. 3.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 15 days (d) 8 days
  4. 4.If 3 notebooks cost ₹12, how much do 11 notebooks cost? (a) ₹44 (b) ₹132 (c) ₹20 (d) ₹48
  5. 5.₹45 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹36 (b) ₹27 (c) ₹9 (d) ₹18
  6. 6.₹64 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹40 (b) ₹32 (c) ₹24 (d) ₹8
  7. 7.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 3 days (d) 10 days
  8. 8.₹308 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹154 (b) ₹56 (c) ₹28 (d) ₹252
  9. 9.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 2 days (b) 12 days (c) 3 days (d) 18 days
  10. 10.If 2 kites cost ₹32, how much do 7 kites cost? (a) ₹224 (b) ₹37 (c) ₹112 (d) ₹128
  11. 11.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 6 days (c) 7 days (d) 5 days
  12. 12.If 4 kites cost ₹100, how much do 2 kites cost? (a) ₹200 (b) ₹50 (c) ₹75 (d) ₹98
  13. 13.If 7 notebooks cost ₹126, how much do 5 notebooks cost? (a) ₹124 (b) ₹630 (c) ₹108 (d) ₹90
  14. 14.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 52 days (c) 7 days (d) 53 days
  15. 15.₹70 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹20 (b) ₹35 (c) ₹50 (d) ₹10
  16. 16.₹432 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹180 (b) ₹216 (c) ₹36 (d) ₹252
  17. 17.If 3 pens cost ₹9, how much do 8 pens cost? (a) ₹72 (b) ₹14 (c) ₹24 (d) ₹27
  18. 18.₹372 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹186 (b) ₹217 (c) ₹31 (d) ₹155
  19. 19.₹611 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹188 (b) ₹47 (c) ₹423 (d) ₹470
  20. 20.If 8 pens cost ₹48, how much do 11 pens cost? (a) ₹528 (b) ₹72 (c) ₹51 (d) ₹66
  21. 21.If 2 mangoes cost ₹36, how much do 3 mangoes cost? (a) ₹54 (b) ₹72 (c) ₹108 (d) ₹37
  22. 22.If 4 kites cost ₹20, how much do 9 kites cost? (a) ₹25 (b) ₹45 (c) ₹50 (d) ₹180
  23. 23.If 7 pens cost ₹49, how much do 12 pens cost? (a) ₹91 (b) ₹84 (c) ₹588 (d) ₹54
  24. 24.₹126 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹63 (b) ₹28 (c) ₹98 (d) ₹14
  25. 25.₹352 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹176 (b) ₹288 (c) ₹32 (d) ₹64
  26. 26.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 4 days (d) 2 days
  27. 27.If 2 pens cost ₹50, how much do 3 pens cost? (a) ₹150 (b) ₹100 (c) ₹75 (d) ₹51
  28. 28.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 17 days (c) 27 days (d) 1 day
  29. 29.₹234 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹234 (b) ₹117 (c) ₹195 (d) ₹39
  30. 30.₹190 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹95 (b) ₹152 (c) ₹38 (d) ₹190
  31. 31.If 7 notebooks cost ₹70, how much do 2 notebooks cost? (a) ₹140 (b) ₹30 (c) ₹20 (d) ₹65
  32. 32.₹351 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹243 (b) ₹270 (c) ₹27 (d) ₹108
  33. 33.If 4 mangoes cost ₹24, how much do 5 mangoes cost? (a) ₹30 (b) ₹120 (c) ₹25 (d) ₹36
  34. 34.If 7 notebooks cost ₹70, how much do 9 notebooks cost? (a) ₹72 (b) ₹630 (c) ₹100 (d) ₹90
  35. 35.If 4 pens cost ₹92, how much do 7 pens cost? (a) ₹184 (b) ₹95 (c) ₹161 (d) ₹644
  36. 36.If 4 kites cost ₹96, how much do 3 kites cost? (a) ₹95 (b) ₹288 (c) ₹96 (d) ₹72
  37. 37.If 9 notebooks cost ₹189, how much do 10 notebooks cost? (a) ₹231 (b) ₹1890 (c) ₹190 (d) ₹210
  38. 38.If 6 mangoes cost ₹90, how much do 4 mangoes cost? (a) ₹75 (b) ₹60 (c) ₹88 (d) ₹360
  39. 39.If 8 kites cost ₹184, how much do 3 kites cost? (a) ₹179 (b) ₹552 (c) ₹92 (d) ₹69
  40. 40.₹70 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹70 (b) ₹56 (c) ₹35 (d) ₹14

Answer key

  1. ₹133
  2. 9 days
  3. 7 days
  4. ₹44
  5. ₹27
  6. ₹40
  7. 2 days
  8. ₹252
  9. 2 days
  10. ₹112
  11. 6 days
  12. ₹50
  13. ₹90
  14. 52 days
  15. ₹50
  16. ₹252
  17. ₹24
  18. ₹217
  19. ₹423
  20. ₹66
  21. ₹54
  22. ₹45
  23. ₹84
  24. ₹98
  25. ₹288
  26. 3 days
  27. ₹75
  28. 3 days
  29. ₹195
  30. ₹152
  31. ₹20
  32. ₹243
  33. ₹30
  34. ₹90
  35. ₹161
  36. ₹72
  37. ₹210
  38. ₹60
  39. ₹69
  40. ₹56

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