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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 569 · 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.If 2 pens cost ₹10, how much do 3 pens cost? (a) ₹20 (b) ₹11 (c) ₹30 (d) ₹15
  2. 2.3 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 4 days (d) 5 days
  3. 3.If 4 pens cost ₹96, how much do 5 pens cost? (a) ₹144 (b) ₹480 (c) ₹97 (d) ₹120
  4. 4.₹308 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹44 (b) ₹176 (c) ₹132 (d) ₹154
  5. 5.If 8 pens cost ₹128, how much do 12 pens cost? (a) ₹132 (b) ₹192 (c) ₹208 (d) ₹1536
  6. 6.If 7 notebooks cost ₹154, how much do 8 notebooks cost? (a) ₹155 (b) ₹1232 (c) ₹176 (d) ₹198
  7. 7.₹182 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹14 (b) ₹70 (c) ₹91 (d) ₹112
  8. 8.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 7 days
  9. 9.If 3 pens cost ₹60, how much do 12 pens cost? (a) ₹720 (b) ₹69 (c) ₹240 (d) ₹260
  10. 10.₹96 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹64 (b) ₹48 (c) ₹32 (d) ₹96
  11. 11.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 17 days (b) 11 days (c) 22 days (d) 21 days
  12. 12.If 2 notebooks cost ₹6, how much do 7 notebooks cost? (a) ₹11 (b) ₹42 (c) ₹24 (d) ₹21
  13. 13.₹162 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹90 (b) ₹18 (c) ₹81 (d) ₹72
  14. 14.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 10 days (d) 11 days
  15. 15.If 4 mangoes cost ₹20, how much do 3 mangoes cost? (a) ₹60 (b) ₹15 (c) ₹19 (d) ₹20
  16. 16.8 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 7 days (d) 6 days
  17. 17.If 6 kites cost ₹126, how much do 7 kites cost? (a) ₹882 (b) ₹168 (c) ₹127 (d) ₹147
  18. 18.₹180 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹54 (b) ₹90 (c) ₹126 (d) ₹18
  19. 19.If 7 kites cost ₹56, how much do 9 kites cost? (a) ₹504 (b) ₹72 (c) ₹58 (d) ₹80
  20. 20.If 7 notebooks cost ₹147, how much do 4 notebooks cost? (a) ₹144 (b) ₹588 (c) ₹84 (d) ₹105
  21. 21.₹650 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹400 (b) ₹50 (c) ₹325 (d) ₹250
  22. 22.If 5 notebooks cost ₹40, how much do 8 notebooks cost? (a) ₹43 (b) ₹64 (c) ₹72 (d) ₹320
  23. 23.If 3 kites cost ₹54, how much do 9 kites cost? (a) ₹60 (b) ₹162 (c) ₹486 (d) ₹180
  24. 24.If 5 notebooks cost ₹65, how much do 11 notebooks cost? (a) ₹71 (b) ₹156 (c) ₹715 (d) ₹143
  25. 25.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 11 days (c) 20 days (d) 5 days
  26. 26.₹112 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹16 (b) ₹32 (c) ₹80 (d) ₹56
  27. 27.If 4 notebooks cost ₹40, how much do 5 notebooks cost? (a) ₹41 (b) ₹60 (c) ₹200 (d) ₹50
  28. 28.₹539 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹245 (b) ₹343 (c) ₹49 (d) ₹294
  29. 29.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 33 days (b) 5 days (c) 34 days (d) 17 days
  30. 30.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 6 days (d) 5 days
  31. 31.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 15 days (c) 16 days (d) 9 days
  32. 32.₹48 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹48 (b) ₹16 (c) ₹32 (d) ₹24
  33. 33.If 7 pens cost ₹140, how much do 8 pens cost? (a) ₹180 (b) ₹160 (c) ₹1120 (d) ₹141
  34. 34.If 3 kites cost ₹12, how much do 8 kites cost? (a) ₹96 (b) ₹17 (c) ₹36 (d) ₹32
  35. 35.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 9 days (c) 13 days (d) 11 days
  36. 36.If 5 notebooks cost ₹100, how much do 6 notebooks cost? (a) ₹101 (b) ₹140 (c) ₹120 (d) ₹600
  37. 37.₹288 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹144 (b) ₹128 (c) ₹32 (d) ₹160
  38. 38.₹120 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹105 (b) ₹15 (c) ₹120 (d) ₹60
  39. 39.₹90 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹90 (b) ₹30 (c) ₹45 (d) ₹60
  40. 40.₹360 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹180 (b) ₹135 (c) ₹225 (d) ₹45

Answer key

  1. ₹15
  2. 4 days
  3. ₹120
  4. ₹176
  5. ₹192
  6. ₹176
  7. ₹112
  8. 5 days
  9. ₹240
  10. ₹64
  11. 21 days
  12. ₹21
  13. ₹90
  14. 10 days
  15. ₹15
  16. 6 days
  17. ₹147
  18. ₹126
  19. ₹72
  20. ₹84
  21. ₹400
  22. ₹64
  23. ₹162
  24. ₹143
  25. 20 days
  26. ₹80
  27. ₹50
  28. ₹294
  29. 33 days
  30. 5 days
  31. 15 days
  32. ₹32
  33. ₹160
  34. ₹32
  35. 16 days
  36. ₹120
  37. ₹160
  38. ₹105
  39. ₹60
  40. ₹225

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