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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 243 · 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. 1.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 3 days (d) 15 days
  2. 2.If 9 kites cost ₹81, how much do 8 kites cost? (a) ₹81 (b) ₹72 (c) ₹80 (d) ₹648
  3. 3.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 21 days (d) 20 days
  4. 4.₹51 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹51 (b) ₹17 (c) ₹35 (d) ₹34
  5. 5.If 5 notebooks cost ₹30, how much do 2 notebooks cost? (a) ₹27 (b) ₹60 (c) ₹12 (d) ₹18
  6. 6.If 8 pens cost ₹88, how much do 4 pens cost? (a) ₹352 (b) ₹44 (c) ₹55 (d) ₹84
  7. 7.₹348 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹145 (b) ₹29 (c) ₹203 (d) ₹174
  8. 8.If 9 pens cost ₹207, how much do 5 pens cost? (a) ₹115 (b) ₹1035 (c) ₹138 (d) ₹203
  9. 9.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 5 days (d) 4 days
  10. 10.If 5 notebooks cost ₹105, how much do 11 notebooks cost? (a) ₹111 (b) ₹1155 (c) ₹252 (d) ₹231
  11. 11.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 25 days (b) 13 days (c) 9 days (d) 17 days
  12. 12.₹423 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹377 (b) ₹376 (c) ₹47 (d) ₹423
  13. 13.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 19 days (d) 2 days
  14. 14.If 7 mangoes cost ₹91, how much do 6 mangoes cost? (a) ₹546 (b) ₹90 (c) ₹91 (d) ₹78
  15. 15.₹72 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹8 (b) ₹56 (c) ₹36 (d) ₹16
  16. 16.If 5 notebooks cost ₹45, how much do 9 notebooks cost? (a) ₹90 (b) ₹49 (c) ₹405 (d) ₹81
  17. 17.If 6 pens cost ₹42, how much do 3 pens cost? (a) ₹39 (b) ₹28 (c) ₹126 (d) ₹21
  18. 18.If 7 notebooks cost ₹133, how much do 8 notebooks cost? (a) ₹171 (b) ₹134 (c) ₹1064 (d) ₹152
  19. 19.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 7 days (d) 8 days
  20. 20.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 11 days (d) 8 days
  21. 21.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 8 days (d) 6 days
  22. 22.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 28 days (c) 16 days (d) 12 days
  23. 23.If 6 kites cost ₹48, how much do 7 kites cost? (a) ₹336 (b) ₹64 (c) ₹49 (d) ₹56
  24. 24.₹650 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹250 (b) ₹325 (c) ₹50 (d) ₹400
  25. 25.If 6 pens cost ₹102, how much do 8 pens cost? (a) ₹153 (b) ₹136 (c) ₹104 (d) ₹816
  26. 26.If 8 mangoes cost ₹80, how much do 6 mangoes cost? (a) ₹78 (b) ₹60 (c) ₹70 (d) ₹480
  27. 27.₹144 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹32 (b) ₹16 (c) ₹112 (d) ₹72
  28. 28.If 2 pens cost ₹24, how much do 9 pens cost? (a) ₹216 (b) ₹108 (c) ₹31 (d) ₹120
  29. 29.If 8 mangoes cost ₹136, how much do 3 mangoes cost? (a) ₹68 (b) ₹408 (c) ₹131 (d) ₹51
  30. 30.₹130 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹80 (b) ₹50 (c) ₹65 (d) ₹10
  31. 31.₹408 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹34 (b) ₹170 (c) ₹238 (d) ₹204
  32. 32.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 9 days (d) 28 days
  33. 33.₹230 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹46 (b) ₹92 (c) ₹115 (d) ₹138
  34. 34.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 12 days (c) 8 days (d) 20 days
  35. 35.If 6 notebooks cost ₹90, how much do 7 notebooks cost? (a) ₹105 (b) ₹120 (c) ₹630 (d) ₹91
  36. 36.If 3 pens cost ₹30, how much do 7 pens cost? (a) ₹80 (b) ₹70 (c) ₹34 (d) ₹210
  37. 37.If 8 kites cost ₹160, how much do 7 kites cost? (a) ₹160 (b) ₹1120 (c) ₹159 (d) ₹140
  38. 38.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 8 days (d) 5 days
  39. 39.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 24 days (d) 25 days
  40. 40.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 10 days (d) 6 days

Answer key

  1. 27 days
  2. ₹72
  3. 20 days
  4. ₹34
  5. ₹12
  6. ₹44
  7. ₹203
  8. ₹115
  9. 5 days
  10. ₹231
  11. 9 days
  12. ₹376
  13. 18 days
  14. ₹78
  15. ₹56
  16. ₹81
  17. ₹21
  18. ₹152
  19. 8 days
  20. 9 days
  21. 7 days
  22. 28 days
  23. ₹56
  24. ₹400
  25. ₹136
  26. ₹60
  27. ₹112
  28. ₹108
  29. ₹51
  30. ₹80
  31. ₹238
  32. 7 days
  33. ₹138
  34. 20 days
  35. ₹105
  36. ₹70
  37. ₹140
  38. 6 days
  39. 24 days
  40. 16 days

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