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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 212 · 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. 1.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 5 days (c) 3 days (d) 4 days
  2. 2.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 2 days (c) 6 days (d) 8 days
  3. 3.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 57 days (c) 56 days (d) 8 days
  4. 4.If 3 pens cost ₹27, how much do 6 pens cost? (a) ₹30 (b) ₹63 (c) ₹54 (d) ₹162
  5. 5.₹350 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹175 (b) ₹150 (c) ₹50 (d) ₹200
  6. 6.₹539 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹49 (b) ₹294 (c) ₹343 (d) ₹245
  7. 7.₹78 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹48 (b) ₹6 (c) ₹30 (d) ₹39
  8. 8.If 2 mangoes cost ₹20, how much do 6 mangoes cost? (a) ₹120 (b) ₹70 (c) ₹60 (d) ₹24
  9. 9.If 9 pens cost ₹126, how much do 6 pens cost? (a) ₹98 (b) ₹123 (c) ₹756 (d) ₹84
  10. 10.₹473 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹215 (b) ₹258 (c) ₹301 (d) ₹43
  11. 11.₹126 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹14 (b) ₹63 (c) ₹70 (d) ₹56
  12. 12.₹308 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹154 (b) ₹84 (c) ₹28 (d) ₹224
  13. 13.₹140 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹90 (b) ₹70 (c) ₹50 (d) ₹10
  14. 14.₹100 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹20 (b) ₹80 (c) ₹50 (d) ₹100
  15. 15.If 2 notebooks cost ₹36, how much do 12 notebooks cost? (a) ₹216 (b) ₹432 (c) ₹46 (d) ₹234
  16. 16.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 25 days (b) 4 days (c) 5 days (d) 16 days
  17. 17.If 2 notebooks cost ₹6, how much do 8 notebooks cost? (a) ₹27 (b) ₹12 (c) ₹48 (d) ₹24
  18. 18.₹21 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹14 (b) ₹7 (c) ₹15 (d) ₹21
  19. 19.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 13 days (c) 29 days (d) 3 days
  20. 20.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 28 days (c) 15 days (d) 3 days
  21. 21.If 6 notebooks cost ₹114, how much do 12 notebooks cost? (a) ₹120 (b) ₹228 (c) ₹247 (d) ₹1368
  22. 22.₹189 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹135 (b) ₹108 (c) ₹27 (d) ₹81
  23. 23.If 9 pens cost ₹144, how much do 8 pens cost? (a) ₹144 (b) ₹143 (c) ₹128 (d) ₹1152
  24. 24.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 8 days (d) 7 days
  25. 25.If 4 pens cost ₹92, how much do 11 pens cost? (a) ₹99 (b) ₹276 (c) ₹1012 (d) ₹253
  26. 26.If 2 mangoes cost ₹46, how much do 10 mangoes cost? (a) ₹230 (b) ₹460 (c) ₹54 (d) ₹253
  27. 27.If 5 notebooks cost ₹125, how much do 12 notebooks cost? (a) ₹132 (b) ₹300 (c) ₹1500 (d) ₹325
  28. 28.₹312 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹120 (b) ₹192 (c) ₹156 (d) ₹24
  29. 29.If 6 notebooks cost ₹48, how much do 4 notebooks cost? (a) ₹46 (b) ₹192 (c) ₹40 (d) ₹32
  30. 30.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 20 days (b) 6 days (c) 15 days (d) 5 days
  31. 31.₹108 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹108 (b) ₹36 (c) ₹72 (d) ₹54
  32. 32.If 8 notebooks cost ₹64, how much do 10 notebooks cost? (a) ₹80 (b) ₹88 (c) ₹66 (d) ₹640
  33. 33.If 9 notebooks cost ₹45, how much do 10 notebooks cost? (a) ₹450 (b) ₹55 (c) ₹50 (d) ₹46
  34. 34.If 6 mangoes cost ₹120, how much do 4 mangoes cost? (a) ₹118 (b) ₹80 (c) ₹480 (d) ₹100
  35. 35.₹105 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹105 (b) ₹91 (c) ₹15 (d) ₹90
  36. 36.If 7 kites cost ₹140, how much do 2 kites cost? (a) ₹135 (b) ₹40 (c) ₹60 (d) ₹280
  37. 37.₹140 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹20 (b) ₹60 (c) ₹80 (d) ₹70
  38. 38.₹360 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹320 (b) ₹180 (c) ₹360 (d) ₹40
  39. 39.If 8 kites cost ₹120, how much do 9 kites cost? (a) ₹1080 (b) ₹121 (c) ₹135 (d) ₹150
  40. 40.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 5 days (d) 9 days

Answer key

  1. 3 days
  2. 8 days
  3. 56 days
  4. ₹54
  5. ₹200
  6. ₹294
  7. ₹48
  8. ₹60
  9. ₹84
  10. ₹258
  11. ₹70
  12. ₹224
  13. ₹90
  14. ₹80
  15. ₹216
  16. 4 days
  17. ₹24
  18. ₹14
  19. 28 days
  20. 27 days
  21. ₹228
  22. ₹108
  23. ₹128
  24. 7 days
  25. ₹253
  26. ₹230
  27. ₹300
  28. ₹192
  29. ₹32
  30. 5 days
  31. ₹72
  32. ₹80
  33. ₹50
  34. ₹80
  35. ₹90
  36. ₹40
  37. ₹80
  38. ₹320
  39. ₹135
  40. 9 days

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