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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 653 · 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. 1.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 8 days (d) 2 days
  2. 2.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 36 days (c) 4 days (d) 6 days
  3. 3.₹56 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹28 (b) ₹8 (c) ₹40 (d) ₹16
  4. 4.₹104 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹72 (b) ₹32 (c) ₹8 (d) ₹52
  5. 5.If 4 kites cost ₹100, how much do 11 kites cost? (a) ₹300 (b) ₹1100 (c) ₹107 (d) ₹275
  6. 6.If 4 kites cost ₹12, how much do 11 kites cost? (a) ₹33 (b) ₹36 (c) ₹19 (d) ₹132
  7. 7.₹66 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹33 (b) ₹6 (c) ₹42 (d) ₹24
  8. 8.If 5 kites cost ₹60, how much do 2 kites cost? (a) ₹57 (b) ₹24 (c) ₹36 (d) ₹120
  9. 9.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 13 days (c) 15 days (d) 22 days
  10. 10.₹228 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹114 (b) ₹95 (c) ₹133 (d) ₹19
  11. 11.If 5 mangoes cost ₹25, how much do 12 mangoes cost? (a) ₹60 (b) ₹65 (c) ₹32 (d) ₹300
  12. 12.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 19 days (c) 4 days (d) 9 days
  13. 13.₹410 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹41 (b) ₹369 (c) ₹410 (d) ₹205
  14. 14.If 7 kites cost ₹98, how much do 9 kites cost? (a) ₹140 (b) ₹882 (c) ₹100 (d) ₹126
  15. 15.₹165 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹15 (b) ₹45 (c) ₹135 (d) ₹120
  16. 16.If 2 kites cost ₹28, how much do 10 kites cost? (a) ₹140 (b) ₹36 (c) ₹154 (d) ₹280
  17. 17.₹290 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹145 (b) ₹261 (c) ₹29 (d) ₹290
  18. 18.If 4 kites cost ₹16, how much do 8 kites cost? (a) ₹128 (b) ₹36 (c) ₹32 (d) ₹20
  19. 19.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 7 days (d) 6 days
  20. 20.₹390 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹30 (b) ₹270 (c) ₹195 (d) ₹120
  21. 21.If 4 mangoes cost ₹20, how much do 2 mangoes cost? (a) ₹18 (b) ₹40 (c) ₹10 (d) ₹15
  22. 22.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 7 days (d) 2 days
  23. 23.₹135 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹15 (b) ₹105 (c) ₹120 (d) ₹30
  24. 24.If 4 notebooks cost ₹24, how much do 3 notebooks cost? (a) ₹24 (b) ₹72 (c) ₹18 (d) ₹23
  25. 25.If 9 notebooks cost ₹54, how much do 12 notebooks cost? (a) ₹57 (b) ₹78 (c) ₹72 (d) ₹648
  26. 26.If 6 notebooks cost ₹84, how much do 9 notebooks cost? (a) ₹756 (b) ₹126 (c) ₹87 (d) ₹140
  27. 27.₹90 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹45 (b) ₹18 (c) ₹54 (d) ₹36
  28. 28.If 6 notebooks cost ₹30, how much do 11 notebooks cost? (a) ₹35 (b) ₹55 (c) ₹60 (d) ₹330
  29. 29.If 5 kites cost ₹15, how much do 10 kites cost? (a) ₹30 (b) ₹33 (c) ₹150 (d) ₹20
  30. 30.If 6 notebooks cost ₹18, how much do 5 notebooks cost? (a) ₹90 (b) ₹18 (c) ₹17 (d) ₹15
  31. 31.If 7 pens cost ₹49, how much do 4 pens cost? (a) ₹196 (b) ₹28 (c) ₹35 (d) ₹46
  32. 32.₹135 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹90 (b) ₹60 (c) ₹15 (d) ₹75
  33. 33.If 4 pens cost ₹52, how much do 11 pens cost? (a) ₹143 (b) ₹572 (c) ₹59 (d) ₹156
  34. 34.₹136 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹85 (b) ₹51 (c) ₹68 (d) ₹17
  35. 35.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 8 days (d) 17 days
  36. 36.If 3 notebooks cost ₹72, how much do 10 notebooks cost? (a) ₹240 (b) ₹720 (c) ₹79 (d) ₹264
  37. 37.If 2 mangoes cost ₹20, how much do 12 mangoes cost? (a) ₹130 (b) ₹120 (c) ₹240 (d) ₹30
  38. 38.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 19 days (c) 2 days (d) 4 days
  39. 39.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 1 day (c) 11 days (d) 3 days
  40. 40.₹338 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹26 (b) ₹130 (c) ₹169 (d) ₹208

Answer key

  1. 8 days
  2. 36 days
  3. ₹40
  4. ₹72
  5. ₹275
  6. ₹33
  7. ₹42
  8. ₹24
  9. 21 days
  10. ₹133
  11. ₹60
  12. 49 days
  13. ₹369
  14. ₹126
  15. ₹120
  16. ₹140
  17. ₹261
  18. ₹32
  19. 6 days
  20. ₹270
  21. ₹10
  22. 3 days
  23. ₹105
  24. ₹18
  25. ₹72
  26. ₹126
  27. ₹54
  28. ₹55
  29. ₹30
  30. ₹15
  31. ₹28
  32. ₹75
  33. ₹143
  34. ₹85
  35. 8 days
  36. ₹240
  37. ₹120
  38. 3 days
  39. 3 days
  40. ₹208

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