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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 633 · 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.₹110 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹44 (b) ₹66 (c) ₹55 (d) ₹22
  2. 2.₹507 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹39 (b) ₹195 (c) ₹351 (d) ₹312
  3. 3.₹351 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹39 (b) ₹156 (c) ₹195 (d) ₹234
  4. 4.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 19 days (b) 9 days (c) 28 days (d) 7 days
  5. 5.If 3 notebooks cost ₹15, how much do 6 notebooks cost? (a) ₹90 (b) ₹35 (c) ₹30 (d) ₹18
  6. 6.₹176 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹64 (b) ₹88 (c) ₹16 (d) ₹112
  7. 7.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 45 days (c) 7 days (d) 23 days
  8. 8.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 26 days (d) 11 days
  9. 9.If 4 pens cost ₹24, how much do 8 pens cost? (a) ₹28 (b) ₹192 (c) ₹54 (d) ₹48
  10. 10.₹256 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹128 (b) ₹256 (c) ₹32 (d) ₹224
  11. 11.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 12 days (c) 9 days (d) 4 days
  12. 12.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 14 days (c) 5 days (d) 15 days
  13. 13.₹154 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹88 (b) ₹22 (c) ₹77 (d) ₹66
  14. 14.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 43 days (c) 42 days (d) 20 days
  15. 15.If 6 notebooks cost ₹84, how much do 8 notebooks cost? (a) ₹672 (b) ₹112 (c) ₹126 (d) ₹86
  16. 16.5 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 14 days (c) 10 days (d) 20 days
  17. 17.If 8 pens cost ₹112, how much do 12 pens cost? (a) ₹116 (b) ₹1344 (c) ₹168 (d) ₹182
  18. 18.If 7 mangoes cost ₹161, how much do 4 mangoes cost? (a) ₹158 (b) ₹92 (c) ₹115 (d) ₹644
  19. 19.₹98 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹14 (b) ₹42 (c) ₹56 (d) ₹49
  20. 20.If 3 kites cost ₹12, how much do 8 kites cost? (a) ₹36 (b) ₹96 (c) ₹32 (d) ₹17
  21. 21.₹440 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹220 (b) ₹40 (c) ₹240 (d) ₹200
  22. 22.If 8 mangoes cost ₹88, how much do 6 mangoes cost? (a) ₹86 (b) ₹66 (c) ₹528 (d) ₹77
  23. 23.If 5 kites cost ₹95, how much do 11 kites cost? (a) ₹101 (b) ₹1045 (c) ₹228 (d) ₹209
  24. 24.₹136 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹136 (b) ₹102 (c) ₹68 (d) ₹34
  25. 25.₹126 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹54 (b) ₹72 (c) ₹18 (d) ₹63
  26. 26.If 8 notebooks cost ₹160, how much do 3 notebooks cost? (a) ₹80 (b) ₹480 (c) ₹60 (d) ₹155
  27. 27.₹320 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹32 (b) ₹320 (c) ₹160 (d) ₹288
  28. 28.If 4 notebooks cost ₹24, how much do 12 notebooks cost? (a) ₹78 (b) ₹72 (c) ₹288 (d) ₹32
  29. 29.If 9 mangoes cost ₹135, how much do 5 mangoes cost? (a) ₹90 (b) ₹131 (c) ₹75 (d) ₹675
  30. 30.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 35 days (c) 15 days (d) 5 days
  31. 31.₹312 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹182 (b) ₹26 (c) ₹156 (d) ₹130
  32. 32.₹297 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹135 (b) ₹27 (c) ₹162 (d) ₹189
  33. 33.If 2 pens cost ₹28, how much do 3 pens cost? (a) ₹84 (b) ₹29 (c) ₹42 (d) ₹56
  34. 34.₹40 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹35 (b) ₹5 (c) ₹40 (d) ₹20
  35. 35.If 9 kites cost ₹36, how much do 6 kites cost? (a) ₹33 (b) ₹216 (c) ₹28 (d) ₹24
  36. 36.If 4 pens cost ₹32, how much do 5 pens cost? (a) ₹160 (b) ₹40 (c) ₹33 (d) ₹48
  37. 37.If 2 mangoes cost ₹30, how much do 3 mangoes cost? (a) ₹60 (b) ₹45 (c) ₹31 (d) ₹90
  38. 38.₹104 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹52 (b) ₹13 (c) ₹91 (d) ₹104
  39. 39.₹180 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹75 (b) ₹90 (c) ₹105 (d) ₹15
  40. 40.₹462 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹42 (b) ₹84 (c) ₹231 (d) ₹378

Answer key

  1. ₹66
  2. ₹312
  3. ₹195
  4. 7 days
  5. ₹30
  6. ₹112
  7. 5 days
  8. 26 days
  9. ₹48
  10. ₹224
  11. 3 days
  12. 14 days
  13. ₹88
  14. 42 days
  15. ₹112
  16. 20 days
  17. ₹168
  18. ₹92
  19. ₹56
  20. ₹32
  21. ₹240
  22. ₹66
  23. ₹209
  24. ₹102
  25. ₹72
  26. ₹60
  27. ₹288
  28. ₹72
  29. ₹75
  30. 35 days
  31. ₹182
  32. ₹162
  33. ₹42
  34. ₹35
  35. ₹24
  36. ₹40
  37. ₹45
  38. ₹91
  39. ₹105
  40. ₹378

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