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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 320 · 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 5 mangoes cost ₹30, how much do 6 mangoes cost? (a) ₹42 (b) ₹180 (c) ₹31 (d) ₹36
  2. 2.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 1 day (b) 10 days (c) 8 days (d) 9 days
  3. 3.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 16 days (d) 11 days
  4. 4.If 8 pens cost ₹64, how much do 4 pens cost? (a) ₹40 (b) ₹60 (c) ₹32 (d) ₹256
  5. 5.If 5 kites cost ₹25, how much do 9 kites cost? (a) ₹225 (b) ₹29 (c) ₹50 (d) ₹45
  6. 6.₹153 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹102 (b) ₹68 (c) ₹85 (d) ₹17
  7. 7.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 22 days (c) 13 days (d) 9 days
  8. 8.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 39 days (c) 17 days (d) 40 days
  9. 9.If 9 notebooks cost ₹117, how much do 2 notebooks cost? (a) ₹26 (b) ₹110 (c) ₹39 (d) ₹234
  10. 10.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 10 days (d) 13 days
  11. 11.If 9 kites cost ₹135, how much do 6 kites cost? (a) ₹810 (b) ₹90 (c) ₹132 (d) ₹105
  12. 12.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 18 days (c) 7 days (d) 11 days
  13. 13.If 8 pens cost ₹120, how much do 7 pens cost? (a) ₹840 (b) ₹119 (c) ₹105 (d) ₹120
  14. 14.₹297 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹243 (b) ₹27 (c) ₹81 (d) ₹216
  15. 15.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 5 days (d) 4 days
  16. 16.If 5 kites cost ₹20, how much do 4 kites cost? (a) ₹20 (b) ₹80 (c) ₹19 (d) ₹16
  17. 17.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 11 days (d) 10 days
  18. 18.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 2 days (c) 11 days (d) 8 days
  19. 19.If 2 mangoes cost ₹42, how much do 11 mangoes cost? (a) ₹252 (b) ₹231 (c) ₹462 (d) ₹51
  20. 20.If 2 mangoes cost ₹10, how much do 8 mangoes cost? (a) ₹45 (b) ₹16 (c) ₹80 (d) ₹40
  21. 21.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 4 days (c) 41 days (d) 16 days
  22. 22.₹270 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹210 (b) ₹135 (c) ₹60 (d) ₹30
  23. 23.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 2 days (d) 3 days
  24. 24.If 9 kites cost ₹180, how much do 3 kites cost? (a) ₹60 (b) ₹174 (c) ₹540 (d) ₹80
  25. 25.If 2 kites cost ₹8, how much do 8 kites cost? (a) ₹14 (b) ₹64 (c) ₹32 (d) ₹36
  26. 26.₹117 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹117 (b) ₹105 (c) ₹13 (d) ₹104
  27. 27.₹205 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹82 (b) ₹123 (c) ₹164 (d) ₹41
  28. 28.4 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) 12 days (d) 16 days
  29. 29.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 40 days (c) 7 days (d) 39 days
  30. 30.₹105 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹75 (b) ₹15 (c) ₹90 (d) ₹30
  31. 31.If 8 kites cost ₹72, how much do 2 kites cost? (a) ₹27 (b) ₹144 (c) ₹18 (d) ₹66
  32. 32.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 3 days (c) 4 days (d) 5 days
  33. 33.If 3 notebooks cost ₹15, how much do 12 notebooks cost? (a) ₹180 (b) ₹65 (c) ₹60 (d) ₹24
  34. 34.₹198 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹108 (b) ₹18 (c) ₹99 (d) ₹90
  35. 35.If 4 notebooks cost ₹76, how much do 2 notebooks cost? (a) ₹57 (b) ₹74 (c) ₹152 (d) ₹38
  36. 36.₹495 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹360 (b) ₹45 (c) ₹315 (d) ₹180
  37. 37.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 45 days (c) 21 days (d) 5 days
  38. 38.If 6 kites cost ₹54, how much do 11 kites cost? (a) ₹99 (b) ₹594 (c) ₹108 (d) ₹59
  39. 39.₹540 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹45 (b) ₹270 (c) ₹315 (d) ₹225
  40. 40.If 7 notebooks cost ₹175, how much do 9 notebooks cost? (a) ₹177 (b) ₹225 (c) ₹1575 (d) ₹250

Answer key

  1. ₹36
  2. 9 days
  3. 15 days
  4. ₹32
  5. ₹45
  6. ₹85
  7. 22 days
  8. 39 days
  9. ₹26
  10. 9 days
  11. ₹90
  12. 18 days
  13. ₹105
  14. ₹216
  15. 5 days
  16. ₹16
  17. 10 days
  18. 10 days
  19. ₹231
  20. ₹40
  21. 40 days
  22. ₹210
  23. 3 days
  24. ₹60
  25. ₹32
  26. ₹104
  27. ₹123
  28. 28 days
  29. 39 days
  30. ₹75
  31. ₹18
  32. 4 days
  33. ₹60
  34. ₹108
  35. ₹38
  36. ₹315
  37. 45 days
  38. ₹99
  39. ₹315
  40. ₹225

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