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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 608 · 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.₹189 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹21 (b) ₹168 (c) ₹42 (d) ₹147
  2. 2.If 9 pens cost ₹81, how much do 12 pens cost? (a) ₹84 (b) ₹117 (c) ₹972 (d) ₹108
  3. 3.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 8 days (d) 13 days
  4. 4.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 1 day (d) 10 days
  5. 5.₹55 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹35 (b) ₹5 (c) ₹30 (d) ₹25
  6. 6.If 7 pens cost ₹35, how much do 9 pens cost? (a) ₹45 (b) ₹37 (c) ₹50 (d) ₹315
  7. 7.₹585 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹45 (b) ₹180 (c) ₹450 (d) ₹405
  8. 8.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 45 days (c) 11 days (d) 5 days
  9. 9.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 6 days (d) 2 days
  10. 10.₹288 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹108 (b) ₹180 (c) ₹144 (d) ₹36
  11. 11.If 2 pens cost ₹44, how much do 12 pens cost? (a) ₹528 (b) ₹54 (c) ₹286 (d) ₹264
  12. 12.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 13 days (c) 10 days (d) 17 days
  13. 13.If 9 pens cost ₹171, how much do 10 pens cost? (a) ₹190 (b) ₹172 (c) ₹1710 (d) ₹209
  14. 14.₹396 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹252 (b) ₹144 (c) ₹36 (d) ₹198
  15. 15.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 24 days (c) 4 days (d) 12 days
  16. 16.If 6 pens cost ₹120, how much do 10 pens cost? (a) ₹220 (b) ₹1200 (c) ₹200 (d) ₹124
  17. 17.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 17 days (c) 16 days (d) 1 day
  18. 18.If 2 notebooks cost ₹40, how much do 9 notebooks cost? (a) ₹200 (b) ₹180 (c) ₹360 (d) ₹47
  19. 19.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 25 days (b) 17 days (c) 13 days (d) 9 days
  20. 20.If 4 notebooks cost ₹96, how much do 12 notebooks cost? (a) ₹104 (b) ₹288 (c) ₹312 (d) ₹1152
  21. 21.If 3 notebooks cost ₹15, how much do 9 notebooks cost? (a) ₹50 (b) ₹135 (c) ₹21 (d) ₹45
  22. 22.If 2 kites cost ₹26, how much do 6 kites cost? (a) ₹30 (b) ₹156 (c) ₹78 (d) ₹91
  23. 23.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 28 days (d) 15 days
  24. 24.If 9 pens cost ₹216, how much do 2 pens cost? (a) ₹432 (b) ₹72 (c) ₹209 (d) ₹48
  25. 25.₹240 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹120 (b) ₹140 (c) ₹100 (d) ₹20
  26. 26.₹140 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹70 (b) ₹14 (c) ₹126 (d) ₹140
  27. 27.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 14 days (b) 5 days (c) 20 days (d) 6 days
  28. 28.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 12 days
  29. 29.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 6 days (c) 12 days (d) 18 days
  30. 30.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹40 (b) ₹48 (c) ₹8 (d) ₹44
  31. 31.₹154 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹77 (b) ₹28 (c) ₹126 (d) ₹14
  32. 32.₹352 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹132 (b) ₹220 (c) ₹176 (d) ₹44
  33. 33.If 8 notebooks cost ₹72, how much do 7 notebooks cost? (a) ₹63 (b) ₹504 (c) ₹71 (d) ₹72
  34. 34.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 14 days (d) 5 days
  35. 35.If 9 kites cost ₹54, how much do 3 kites cost? (a) ₹48 (b) ₹162 (c) ₹18 (d) ₹24
  36. 36.If 2 notebooks cost ₹20, how much do 4 notebooks cost? (a) ₹22 (b) ₹50 (c) ₹80 (d) ₹40
  37. 37.₹88 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹33 (b) ₹11 (c) ₹55 (d) ₹44
  38. 38.₹77 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹7 (b) ₹28 (c) ₹49 (d) ₹56
  39. 39.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 9 days
  40. 40.₹168 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹120 (b) ₹24 (c) ₹84 (d) ₹48

Answer key

  1. ₹147
  2. ₹108
  3. 9 days
  4. 9 days
  5. ₹30
  6. ₹45
  7. ₹405
  8. 45 days
  9. 8 days
  10. ₹180
  11. ₹264
  12. 10 days
  13. ₹190
  14. ₹252
  15. 24 days
  16. ₹200
  17. 16 days
  18. ₹180
  19. 25 days
  20. ₹288
  21. ₹45
  22. ₹78
  23. 27 days
  24. ₹48
  25. ₹140
  26. ₹126
  27. 5 days
  28. 6 days
  29. 18 days
  30. ₹48
  31. ₹126
  32. ₹220
  33. ₹63
  34. 14 days
  35. ₹18
  36. ₹40
  37. ₹55
  38. ₹49
  39. 7 days
  40. ₹120

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