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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 74 · 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.₹42 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹14 (b) ₹42 (c) ₹21 (d) ₹28
  2. 2.If 6 mangoes cost ₹54, how much do 3 mangoes cost? (a) ₹51 (b) ₹36 (c) ₹27 (d) ₹162
  3. 3.If 3 kites cost ₹66, how much do 7 kites cost? (a) ₹70 (b) ₹154 (c) ₹462 (d) ₹176
  4. 4.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 20 days (c) 7 days (d) 13 days
  5. 5.₹336 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹48 (b) ₹336 (c) ₹288 (d) ₹168
  6. 6.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 9 days (d) 8 days
  7. 7.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 9 days (d) 4 days
  8. 8.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 6 days (c) 7 days (d) 5 days
  9. 9.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 8 days (c) 20 days (d) 56 days
  10. 10.If 8 notebooks cost ₹176, how much do 5 notebooks cost? (a) ₹880 (b) ₹132 (c) ₹110 (d) ₹173
  11. 11.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 3 days (d) 14 days
  12. 12.If 2 mangoes cost ₹22, how much do 3 mangoes cost? (a) ₹33 (b) ₹66 (c) ₹23 (d) ₹44
  13. 13.₹245 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹105 (b) ₹175 (c) ₹140 (d) ₹35
  14. 14.If 3 kites cost ₹36, how much do 12 kites cost? (a) ₹45 (b) ₹156 (c) ₹144 (d) ₹432
  15. 15.₹248 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹248 (b) ₹217 (c) ₹124 (d) ₹31
  16. 16.If 2 mangoes cost ₹6, how much do 10 mangoes cost? (a) ₹33 (b) ₹14 (c) ₹30 (d) ₹60
  17. 17.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 4 days (d) 12 days
  18. 18.₹624 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹192 (b) ₹432 (c) ₹312 (d) ₹48
  19. 19.If 2 mangoes cost ₹34, how much do 11 mangoes cost? (a) ₹43 (b) ₹187 (c) ₹374 (d) ₹204
  20. 20.If 2 kites cost ₹12, how much do 8 kites cost? (a) ₹18 (b) ₹54 (c) ₹48 (d) ₹96
  21. 21.₹564 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹235 (b) ₹282 (c) ₹47 (d) ₹329
  22. 22.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 4 days (d) 17 days
  23. 23.If 3 notebooks cost ₹72, how much do 9 notebooks cost? (a) ₹78 (b) ₹216 (c) ₹648 (d) ₹240
  24. 24.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 15 days (d) 21 days
  25. 25.If 7 kites cost ₹154, how much do 11 kites cost? (a) ₹158 (b) ₹264 (c) ₹242 (d) ₹1694
  26. 26.If 7 notebooks cost ₹175, how much do 12 notebooks cost? (a) ₹325 (b) ₹180 (c) ₹2100 (d) ₹300
  27. 27.If 5 mangoes cost ₹20, how much do 8 mangoes cost? (a) ₹36 (b) ₹23 (c) ₹32 (d) ₹160
  28. 28.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 11 days (d) 1 day
  29. 29.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 2 days (d) 3 days
  30. 30.7 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
  31. 31.If 4 notebooks cost ₹28, how much do 5 notebooks cost? (a) ₹140 (b) ₹29 (c) ₹35 (d) ₹42
  32. 32.₹414 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹46 (b) ₹207 (c) ₹230 (d) ₹184
  33. 33.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 15 days (c) 4 days (d) 10 days
  34. 34.₹147 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹98 (b) ₹147 (c) ₹49 (d) ₹99
  35. 35.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 22 days (b) 9 days (c) 21 days (d) 15 days
  36. 36.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 9 days (d) 17 days
  37. 37.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 8 days (c) 6 days (d) 7 days
  38. 38.If 8 notebooks cost ₹88, how much do 7 notebooks cost? (a) ₹77 (b) ₹616 (c) ₹87 (d) ₹88
  39. 39.If 4 pens cost ₹80, how much do 5 pens cost? (a) ₹100 (b) ₹81 (c) ₹120 (d) ₹400
  40. 40.If 5 mangoes cost ₹50, how much do 7 mangoes cost? (a) ₹52 (b) ₹70 (c) ₹80 (d) ₹350

Answer key

  1. ₹28
  2. ₹27
  3. ₹154
  4. 5 days
  5. ₹288
  6. 8 days
  7. 4 days
  8. 6 days
  9. 56 days
  10. ₹110
  11. 14 days
  12. ₹33
  13. ₹140
  14. ₹144
  15. ₹217
  16. ₹30
  17. 12 days
  18. ₹432
  19. ₹187
  20. ₹48
  21. ₹329
  22. 5 days
  23. ₹216
  24. 21 days
  25. ₹242
  26. ₹300
  27. ₹32
  28. 21 days
  29. 3 days
  30. 7 days
  31. ₹35
  32. ₹230
  33. 14 days
  34. ₹98
  35. 21 days
  36. 9 days
  37. 7 days
  38. ₹77
  39. ₹100
  40. ₹70

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