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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 611 · 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.₹217 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹31 (b) ₹93 (c) ₹124 (d) ₹155
  2. 2.₹54 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹27 (b) ₹45 (c) ₹9 (d) ₹54
  3. 3.If 9 kites cost ₹171, how much do 3 kites cost? (a) ₹76 (b) ₹513 (c) ₹57 (d) ₹165
  4. 4.₹336 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹168 (b) ₹48 (c) ₹288 (d) ₹336
  5. 5.₹161 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹23 (b) ₹115 (c) ₹92 (d) ₹69
  6. 6.₹351 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹243 (b) ₹135 (c) ₹27 (d) ₹216
  7. 7.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 22 days (c) 21 days (d) 11 days
  8. 8.If 2 mangoes cost ₹14, how much do 5 mangoes cost? (a) ₹17 (b) ₹35 (c) ₹70 (d) ₹42
  9. 9.₹42 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹21 (b) ₹36 (c) ₹42 (d) ₹6
  10. 10.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 45 days (b) 21 days (c) 9 days (d) 5 days
  11. 11.If 2 kites cost ₹10, how much do 12 kites cost? (a) ₹65 (b) ₹120 (c) ₹20 (d) ₹60
  12. 12.If 5 mangoes cost ₹15, how much do 10 mangoes cost? (a) ₹20 (b) ₹33 (c) ₹150 (d) ₹30
  13. 13.₹250 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹125 (b) ₹50 (c) ₹200 (d) ₹250
  14. 14.₹329 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹283 (b) ₹329 (c) ₹47 (d) ₹282
  15. 15.₹387 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹387 (b) ₹344 (c) ₹43 (d) ₹345
  16. 16.If 3 pens cost ₹54, how much do 5 pens cost? (a) ₹270 (b) ₹90 (c) ₹108 (d) ₹56
  17. 17.₹189 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹147 (b) ₹21 (c) ₹42 (d) ₹168
  18. 18.₹121 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹55 (b) ₹11 (c) ₹66 (d) ₹77
  19. 19.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 1 day (c) 7 days (d) 10 days
  20. 20.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 2 days (d) 7 days
  21. 21.If 6 pens cost ₹30, how much do 4 pens cost? (a) ₹120 (b) ₹20 (c) ₹28 (d) ₹25
  22. 22.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 5 days (d) 7 days
  23. 23.If 5 mangoes cost ₹20, how much do 3 mangoes cost? (a) ₹12 (b) ₹16 (c) ₹18 (d) ₹60
  24. 24.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 12 days (d) 8 days
  25. 25.₹276 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹46 (b) ₹276 (c) ₹230 (d) ₹138
  26. 26.₹70 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹10 (b) ₹35 (c) ₹30 (d) ₹40
  27. 27.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 12 days (c) 3 days (d) 2 days
  28. 28.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 8 days (c) 42 days (d) 43 days
  29. 29.If 5 pens cost ₹55, how much do 12 pens cost? (a) ₹62 (b) ₹143 (c) ₹132 (d) ₹660
  30. 30.₹154 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹70 (b) ₹84 (c) ₹77 (d) ₹14
  31. 31.If 4 notebooks cost ₹20, how much do 5 notebooks cost? (a) ₹25 (b) ₹30 (c) ₹100 (d) ₹21
  32. 32.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 31 days (b) 11 days (c) 19 days (d) 30 days
  33. 33.₹252 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹126 (b) ₹180 (c) ₹36 (d) ₹72
  34. 34.₹252 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹144 (b) ₹36 (c) ₹108 (d) ₹126
  35. 35.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 6 days (d) 9 days
  36. 36.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 20 days (c) 5 days (d) 7 days
  37. 37.₹351 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹27 (b) ₹243 (c) ₹270 (d) ₹108
  38. 38.If 4 pens cost ₹52, how much do 7 pens cost? (a) ₹55 (b) ₹364 (c) ₹91 (d) ₹104
  39. 39.If 5 notebooks cost ₹75, how much do 6 notebooks cost? (a) ₹450 (b) ₹76 (c) ₹90 (d) ₹105
  40. 40.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 3 days (d) 2 days

Answer key

  1. ₹124
  2. ₹45
  3. ₹57
  4. ₹288
  5. ₹92
  6. ₹216
  7. 21 days
  8. ₹35
  9. ₹36
  10. 45 days
  11. ₹60
  12. ₹30
  13. ₹200
  14. ₹282
  15. ₹344
  16. ₹90
  17. ₹147
  18. ₹66
  19. 10 days
  20. 8 days
  21. ₹20
  22. 6 days
  23. ₹12
  24. 8 days
  25. ₹230
  26. ₹40
  27. 3 days
  28. 42 days
  29. ₹132
  30. ₹84
  31. ₹25
  32. 30 days
  33. ₹180
  34. ₹144
  35. 8 days
  36. 5 days
  37. ₹243
  38. ₹91
  39. ₹90
  40. 3 days

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