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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 657 · 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.₹140 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹20 (b) ₹140 (c) ₹120 (d) ₹70
  2. 2.₹286 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹143 (b) ₹176 (c) ₹22 (d) ₹110
  3. 3.₹75 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹45 (b) ₹60 (c) ₹15 (d) ₹30
  4. 4.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 2 days (c) 16 days (d) 13 days
  5. 5.If 4 notebooks cost ₹88, how much do 3 notebooks cost? (a) ₹88 (b) ₹87 (c) ₹264 (d) ₹66
  6. 6.₹225 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹25 (b) ₹200 (c) ₹175 (d) ₹50
  7. 7.6 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
  8. 8.If 7 kites cost ₹168, how much do 3 kites cost? (a) ₹164 (b) ₹504 (c) ₹96 (d) ₹72
  9. 9.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 48 days (c) 3 days (d) 18 days
  10. 10.₹54 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹27 (b) ₹48 (c) ₹6 (d) ₹54
  11. 11.If 8 kites cost ₹64, how much do 12 kites cost? (a) ₹68 (b) ₹768 (c) ₹96 (d) ₹104
  12. 12.₹517 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹282 (b) ₹329 (c) ₹47 (d) ₹235
  13. 13.If 4 notebooks cost ₹64, how much do 8 notebooks cost? (a) ₹68 (b) ₹512 (c) ₹144 (d) ₹128
  14. 14.₹574 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹41 (b) ₹287 (c) ₹369 (d) ₹205
  15. 15.If 9 notebooks cost ₹189, how much do 11 notebooks cost? (a) ₹252 (b) ₹2079 (c) ₹191 (d) ₹231
  16. 16.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 5 days (d) 16 days
  17. 17.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 15 days (d) 28 days
  18. 18.If 7 pens cost ₹175, how much do 8 pens cost? (a) ₹176 (b) ₹225 (c) ₹1400 (d) ₹200
  19. 19.₹343 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹295 (b) ₹294 (c) ₹343 (d) ₹49
  20. 20.If 7 mangoes cost ₹126, how much do 9 mangoes cost? (a) ₹128 (b) ₹1134 (c) ₹180 (d) ₹162
  21. 21.₹392 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹28 (b) ₹196 (c) ₹140 (d) ₹252
  22. 22.If 6 pens cost ₹144, how much do 3 pens cost? (a) ₹432 (b) ₹141 (c) ₹72 (d) ₹96
  23. 23.If 3 kites cost ₹24, how much do 4 kites cost? (a) ₹96 (b) ₹32 (c) ₹40 (d) ₹25
  24. 24.If 2 kites cost ₹8, how much do 12 kites cost? (a) ₹52 (b) ₹48 (c) ₹18 (d) ₹96
  25. 25.If 9 kites cost ₹144, how much do 10 kites cost? (a) ₹145 (b) ₹1440 (c) ₹160 (d) ₹176
  26. 26.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 17 days (d) 18 days
  27. 27.₹490 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹441 (b) ₹490 (c) ₹49 (d) ₹245
  28. 28.₹72 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹8 (b) ₹32 (c) ₹36 (d) ₹40
  29. 29.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹40 (b) ₹8 (c) ₹44 (d) ₹48
  30. 30.₹630 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹45 (b) ₹405 (c) ₹315 (d) ₹225
  31. 31.₹40 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹40 (b) ₹20 (c) ₹32 (d) ₹8
  32. 32.If 5 pens cost ₹40, how much do 6 pens cost? (a) ₹240 (b) ₹48 (c) ₹56 (d) ₹41
  33. 33.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 19 days (d) 3 days
  34. 34.₹129 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹129 (b) ₹43 (c) ₹87 (d) ₹86
  35. 35.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 6 days (c) 24 days (d) 8 days
  36. 36.If 7 kites cost ₹56, how much do 2 kites cost? (a) ₹16 (b) ₹51 (c) ₹24 (d) ₹112
  37. 37.₹110 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹10 (b) ₹60 (c) ₹55 (d) ₹50
  38. 38.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 16 days (c) 10 days (d) 4 days
  39. 39.If 3 pens cost ₹48, how much do 10 pens cost? (a) ₹176 (b) ₹55 (c) ₹480 (d) ₹160
  40. 40.If 3 pens cost ₹12, how much do 4 pens cost? (a) ₹20 (b) ₹13 (c) ₹48 (d) ₹16

Answer key

  1. ₹120
  2. ₹176
  3. ₹45
  4. 1 day
  5. ₹66
  6. ₹175
  7. 15 days
  8. ₹72
  9. 48 days
  10. ₹48
  11. ₹96
  12. ₹282
  13. ₹128
  14. ₹369
  15. ₹231
  16. 16 days
  17. 27 days
  18. ₹200
  19. ₹294
  20. ₹162
  21. ₹252
  22. ₹72
  23. ₹32
  24. ₹48
  25. ₹160
  26. 18 days
  27. ₹441
  28. ₹40
  29. ₹48
  30. ₹405
  31. ₹32
  32. ₹48
  33. 3 days
  34. ₹86
  35. 6 days
  36. ₹16
  37. ₹60
  38. 16 days
  39. ₹160
  40. ₹16

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